No. In this day and age, this is basically a Salafi idea which is used to justify the belief that reconstructing society as it was during the first four caliphs will fix all the problems in the world.
Since Shi'is do not share the idea that society was ideal or perfect during the first four caliphates, and in fact point to a number of problems during that time, or things which were done which may have been against the Prophet's intent (whether relating to internal matters, such as the caliphate or financial management, or external matters, such as wars), this idea isn't found in Shi'ism.
In fact, we look forward to better times during the advent of the Mahdi (A)!
The Hadeeth which is narrated in Shia and Sunni books is (My Ummah will be divided in to seventy three sects). The additional words which you quoted are not authentic. Obviously, the followers of the Quran and the Progeny of the Prophet (SAWA) will be saved because they are the real followers of the Prophet (SAWA).
There are many narrations in Sunni and Shia books regarding the 73 sects, but most of the narrations have additions which are not authentic especially what is in some Sunni books that the saved sect will be those who follow me and my companions ما أنا عليه وأصحابي. Leading Sunni Ulama stated that this narration is fabricated.
Our Shia Ulama narrated many narrations about the 73 sects as find in Bisharat Al-Mustafa narrated from Ameerul Mo'mineen (AS) which states that saved sect will be those who follow the real successor of the Prophet (SAWA).
This narration does not mean that all Muslim sects will be in hellfire except one sect, but means that there will be right sect despite of the different sects. The followers of the right sect will be saved because there have obeyed the orders of Allah (SWT) and the Prophet (SAWA).
In the name of Allah
Such Hadith is not narrated in major Shia sources.
However, there is a similar Hadith in the more recent Shia books (like Bihar al-Anwar), narrated (without a chain) from the Prophet -peace be upon him and his Ahlul Bayt- that conveys a different meaning:
عُلَمَاءُ أُمَّتِي كَأَنْبِيَاءِ بَنِي إِسْرَائِيلَ
The Scholars of My Ummah are like the prophets of Bani-Israel.
This hadith does not state superiority, but similarity. There are different interpretations as to the meaning of this analogy and to whom the prophet is referring when he says "Scholars".
Some experts believe that "scholars" is only referring to the Infallible Imams, and the hadith means that the Imams are Hujjah (Proofs of Allah) to the people, just as those prophets were Hujjah to the people of their time.
Other experts expand the meaning to non-infallible scholars and belive the hadith is stating that just as those prophets were guardians of their people's faith and beliefs, Islamic scholars will guard and preserve the religiosity and beliefs of the Muslim community.
The abovementioned Hadith is narrated in:
Bihar al-Anwar - v2, p22
Mustadrak ul-Wasail - v17, p320
While I believe strongly in the concept of Muslim unity and that we are meant to have brotherhood and sisterhood as one ummah, the reality is, there are rather significant differences in the Shi'i and Sunni heritages (theology, practice, hadith, scholarship, viewpoints on history, worldview, etc), as well as between different subgroups of Shi'is and different subgroups of Sunnis.
If one takes away the all differences, one is really left with very little that is substantial and/or a completely new ideology and new group. For instance, Shi'is and Sunnis have different collections of hadith, and will never entirely adopt each other's. If you take away all the hadith in the name of unity, then you are left with the Qur'an-only view of Islam, which is its own separate ideology.
Also, usually, "just Muslim" is just a code word for "Sunni". This is because what is done by the majority is seen as "normal" and what is done by the minority is seen as "weird" or "deviant". The vast majority of people who are "just Muslim" adopt an overall Sunni worldview and consider any Shi'i-specific views or practices - such as belief in the 12 Imams as an essential part of Islam or the Shi'i timings for breaking fast - to be deviant or optional.
So, there is no real merit to taking away the religious heritage in the name of unity. It is better just to encourage a spirit of tolerance and acceptance of diversity. That is, just because some of my beliefs and practices are different from those of a Sunnni does not mean that we cannot have mutual respect or friendship. In fact, true friendship is based on accepting differences, not forcing people to be identical.
I believe that if we have a spirit of tolerance, friendship, and acceptance of differences, then we can still have brotherhood and sisterhood in the ideal of the ummah. However, this spirit of tolerance needs to go both ways; it cannot be one-sided to work.
There are narrations in both Sunni and Shi'i collections that say that this ummah will divide into seventy-three sects, with only one being saved, i.e. 'the jama'a'. This has been interpreted to mean 'the majority' by Sunni scholars, whereas Imam 'Ali (as) has said that 'the jama'a' are those who follow the truth, even if they are few. This means that, even among the Shi'a, not all will necessarily be among the jama'a. Imam al-Baqir (as) has said 'the fitna is inevitable'. The Qur'an talks about previous generations that attacked their prophets and became divided over their message. There are many reasons for divisions to occur, but one key reason seems to have been for the Arabs to overcome their tribal pride and accept Imam 'Ali (as) as the successor. The Jews and Christians also hid parts of their prophets' messages or changed them, because they thought that their worldly position was jeopardised by challenging aspects of these messages. People are often happy to accept the message as long as they can maintain their worldly status and comforts.
Thank you for your question. The Imam (af) cannot act to his full effectiveness without the support of the Ummah itself and so it is the Ummah that has chosen this situation for itself. In the same way, the Imams could not prevent the cruelty of the Ummayid and Abbasid dynasties or the injustice of some of the prior leaders as these are the leaders that the Ummah had chosen for themselves in rejecting the leadership of the Imams (as). The injustice in this time is a natural consequence of the physical absence of the Imam (af).
May you always be successful.
As Allah is always supporting the Truth against evil, Imam Al-Mahdi ( AS) being the best Servant of Allah in this time, is always acting against injustice and defending the Ummah against cruelty in ways best known to Allah ( SWT).
When we don’t know how Allah (SWT) is supporting the Truth against the evil in our time, we should not claim that Allah is not defending the Ummah against cruelty.
Same exactly is the situation with The Most Humble Servant of Allah, Imam Al-Mahdi, who is the Divine Leader appointed by Allah ( SWT).