Question 1) Can I host it in one of the cloud services?
Yeah, absolutely. It doesn't really matter what platform you're talking about, either. Win/Lin/etc are all able to be hosted. The Cloud Computing group in Google Groups has a good list of cloud platforms, if you're looking for options.
Question 2) Will the cloud service be reliable over a long time?
That's a harder question to answer. The end result is that we won't know until it fails, which leads to the logical conclusion that you should select a provider with a strong background of service and dedication to clients.
One of my biggest concerns is making sure there's an exit strategy from whichever cloud you select. If you're rolling in the bucks (which nearly no one is), consider using two cloud providers much in the same way that you might have, at one point, considered using two data centers. If one fails, you've got a standby solution in short order.