As a corollary to this question, if a woman goes to Mikvah for her conversion "during her period" (let's say on the 2nd or 3rd day), but for some reason (for which she should probably consult her OB/GYN), she doesn't see any blood from the moment she emerges from the Mikvah, is she Tehorah? Does she need to count 7 clean days and then go to the Mikvah again? Does she need to wait a minimum number of days from the onset of her period before she can count those days? If she sees blood after Mikvah, does that begin a new Niddah period with a minimum number of days like a normal Niddah?
Rav Yehuda Hertzl Henkin's (Benei Vanim 2:31) discussion of a related case indicates that she is Tehorah as all bleeding before going to the Mikva is Halachically insignificant.
(The case there is whether a pregnant woman converting needs to worry about Dam Chimmud before marrying her Jewish partner.)