Not in this story. There is AU novel, where he can.
From the unofficial translation of the novel, Vol 6 (iirc) did talk if a pregnancy is possible. Well, a pregnancy from two alphas is possible in very very rare cases and unfortunately, Ash and Karlyle aren't of those few cases. These cases also only happened between a male alpha and female alpha and in their universe, there's still no recorded cases of a male alpha giving birth so the possibility is almost near impossible. It is impossible as Karlyle doesn't have a uterus.
Alice (Karlyle's mom) is one of those rare cases as she and her husband are both alphas. She was also the person that was really worried when news came out the Karlyle might be pregnant. Her worry mostly stems with her own experience being a female alpha giving birth and she recalls how the process was hard for her. She had a high risk of miscarriage and it was very painful for her so she fears what Karlyle, a male alpha, would go through.
But there's an AU in which he does get pregnant but I haven't read it.
I think Lyle can bear children if Ash bit his nape? I read something abouth alpha x alpha rs and the recessive alpha became an omega