Brahmavadini women are women who learn the Vedas, recite mantras, and do Yajnas, as stated here.
My question is, can they marry and have sex with their husbands?
According to the translator's note of the Mitakshara, they can:
Are Brahmavadini women allowed to marry and have sex?
Yes, and in fact, I think they are required to as a duty in marriage.
From the Mahabharata on the story between Agastya and Lopamudra:
After a considerable time, O king, the illustrious Rishi [Agastya] one day beheld Lopamudra, blazing in ascetic splendour come up after the bath in her season. And pleased with the girl, for her services, her purity, and self control, as also with her grace and beauty, he summoned her for marital intercourse.