Not the ones you can afford. Well, not the ones I can afford anyway. There are some higher end ones that do print too.
On the heat press, that's what I've done. I started as an embroidery shop. Then after getting the bug from here decided on adding heat pressing. I knew nothing at all when I did it, but now realize that there really isn't that much to know once you get the basics. Yesterday I purchased a vinyl cutter (needs blade and blade guard replaced) and a 4 color/4 pallet screen printing setup.
I'm going to be busy just learning. But here's what I know... a heat press can be used for 3 different things. 1. press transfers. 2. Press vinyl. 3. Cure ink on screen printed shirts (with a cover sheet). It's a pretty nice multi-tasker. I've been pretty leery about printing my own transfers because it seems like there is a LOT of problems people have from printing to them completely coming off after the first wash. I don't sell anything that I can't stand behind. Plastisol transfers work great. I know cad printz works pretty well too for lifelike printing. I don't think you can really go wrong with a good heat press. I'd get a good 16x20 that swings, but you may not find one within your price range. If I were you I'd wait it out and keep your craigslist searches going at a minimum every hour. I've got an app on my phone that does all that for me. Something will pop up. Also check industrial auctions they pop up sometimes too. You'll get it MUCH cheaper at an industrial auction than anywhere. Especially if it's no bidding online.
So, yes get the press, but don't just settle for cheap. If you wait it out you'll be able to get a great press used for about what a chinese press costs. Trust me, you'll be able to get your money out of a dependable press than chinese press.
Good luck! Unless you're in my area...