No, not at all likely, given Kouta's social status and age. (I'm not sure about statutory rape laws in Japan, but Michi's too young to consent, no matter how she feels.) It would not be a good time for Kouta to find out the identity of the White Rider.

At least Michi is intelligent enough to keep this from happening. Takatora might find out about her being Ryugen, but she wouldn't go into details for her own sake (an for the safety of her team).