As far as I'm aware, there was no drug treatment in the 1930s. However, blood transfusion became generally available, as techniques for storing blood were developed.
Around 1990 I worked on the HIV haemophilia litigation (my boss acted for the Newcastle Haemophilia Centre, which was one of the defendants). Part of my involvement was going through the medical records of the haemophiliacs treated in Newcastle, and it was noticeable thaat all of them who were more than 30-ish had had long periods in hospital as boys as a result of bleeds, and wrecked joints. By contrast, the ones in their early 20s and younger had been on Factor VIII virtually all their lives and were much less badly affected by the haemophilia. They had to avoid contact sports, but their education had not been messed up, they had proper jobs (one was a physiotherapist, another a geologist).
So I think Alexei would have had to have lived until the 1960s or later, and by then the damage would have been done. Bear in mind that Alfonso, his brother and Rupert of Teck all died as a result of car accidents. Alexei would, I think, have become a fast driver in adult life.
Ann