That's long enough to knock out a few kids. Although I heard once that he had an undescended testicle that might have further reduced his chances to breed. Though I don't know if that was true.
Firstly him has anyway find acceptable wife. And I am not sure if any royal house is very intrested about giving their daughters to guy whom has horrible illness which can pass to next generation. And even if Alexei's testicles are totally fine it doesn't mean that he would get son very soon.