I do to a point.
For example, I recently bought Fallen Enchantress. I didn't buy it because I wanted to play Fallen Enchantress. I bought it because Sins of a Solar Empire was beyond awesome and I had automatic faith that Ironclad Games had made another good game the instant I saw Fallen Enchantress, and even though I knew very little about the game, I bought it about 50% to support Ironclad in the hopes they'd make something else I want to play.
That said, I'm not really a fan of turn-based strategy (aside from Civ 3/4/5) but I have to say I really like it. I don't even know why I like it. I've played games almost identical to this before and hated them, but for whatever reason I really like Fallen Enchantress.
But I didn't buy it because I really wanted it. I bought it about half out of encouragement to the devs and half on faith that it's a strat game of some sort from people who already showed me they know how to make a good strat game.
That said, I've only ever done a purchase "on faith" one other time and that was Mass Effect 3. In retrospect, it was still worth it (even though I hated the endings I still enjoyed the bulk of the game and the DLC has all been great) but I would have waited until it went on sale and made sure they got decidedly less of my money than they did.
So...normally no, but if I know a studio has a solid track record of releasing awesome games, yes, I'll buy a game I might never play to support them. But not to the tune of a full $50+ release.