How do you think the Targaryen monarchy would have fared if Daeron the Drunken didn’t die prematurely and succeeded Maekar, but had the same personality?

Very poorly. Daeron’s alcoholism is ultimately secondary to his psychological alienation from his oneiromancy and his Targaryen heritage more broadly, and even putting those aside he’s an extremely passive and uncertain person who can’t stand up to anybody. 

In OTL, he drank and screwed himself to death as quickly as possible even when he was merely a crown prince. Put him on the throne and that would only be intensified.