I thought about the same question before. The answer is yes, I would be more likely to play a game just because it has a browser version. HOWEVER, very few games are small enough to have a browser version run on itch (500mb size limit). So I could also be playing the game because I am specifically looking for a small and casual type of game, not JUST because I've been swindled by "play in browsr".
edit: Ok, maybe not "very few games" but "not every game".