Hmm... tough to say*. You'd have to have a couple of changes in Europe first: keeping the Spanish out of Gibraltar being the absolute first step, and probably a more adventurous middle class for the Ottomans as well. Once they're in the Americas, again, a good deal is up to chance: most colonies didn't make it. But assuming they keep up the effort (say, grabbing some carribean sugar islands, maybe? They tended to get colonised easier, at any rate) they might have a chance of holding onto it, although again there's a lot of luck involved.
*But then that's my answer to everything.
I can't really see the Ottomans developing a New World Empire, though. Some Carribean islands and maybe a New Sweden-sized mainland colony. the
real fun comes if they start trying to conver the natives.
(And if anyone bashes this, you have
precedents.

)