May a husband divorce a pregnant wife?

Yes; talaq while the wife is pregnant is valid and is not a talaq bid'i.
The ʿiddah of a pregnant wife ends when she gives birth, whether that period is long or short. Throughout the pregnancy, the former husband must provide maintenance and housing even if the talaq is irrevocable (ba'in). After the birth, if the wife breastfeeds the child, the husband must pay for the breastfeeding if agreed.
However, the husband should weigh the emotional effect on a pregnant wife. Counselling is encouraged before a final decision. See ʿiddah & rujuk and custody (hadhanah) & lineage.