women - Can a woman converting to Judaism go to the Mikvah during her period?

When Gentiles convert to Judaism, they are "like a newborn".

If I understand correctly, there is no such thing as Niddah vis a vis non-Jews.

So, if I add those two together, I am inclined to assume that if a woman has just finished her period when she goes to the Mikvah for her conversion, not only is she Jewish, but she is in a state of purity from the very start, without counting 7 clean days, etc.

If that assumption is correct, what about if she were to go to Mikvah during her period? Would her conversion be valid, or would her ongoing (or, really, new) state of impurity invalidate the immersion and, by extension, the conversion?

Answer

According an unsourced answer on Yoatzot.org, yes she can, even with active bleeding. I'm wondering why active bleeding wouldn't have Chatzizah problems, though.

The link to the answer has died in their recent reorganization of their Q & A section.