Yes, actually it is mustahabb to do wudu and recite du'a at prayer times.
However you will not technically be in a state of wudu until after the monthly cycle has passed and you have done ghusl, it is just for spiritual/physical cleansing.
However you should not recite the ayat for which sadjah is mandatory and it is said that one should be in a state of purification to recite Du'a al-Mashlool (which you probably aren't reciting before sleeping anyway!).