Could a victorious Beatty become prime minister?

Could a victorious Beatty become prime minister in this timeline?

Possibly, but Beatty appears to have wanted supreme naval command rather than the premiership.

Taking Constantinople might carry Beatty into Downing Street because of his prestige and political connections, but he does not appear to have wanted the office. In this counterfactual, Beatty still seeks the highest naval authority and would regard becoming prime minister as a step away from his preferred role.