Yes. You have complete control--that's the nice bit. The trade-off is that you're the system admin.
Make sure you get a Micro instance. Only some OS fall into the free tier. If you're new to this sort of thing, I'd recommed getting an Ubuntu server because A) it's a good platform and B) there's a huge and very helpful user community.
Also, you might take a look at installing Cherokee server: http://www.cherokee-project.com/ It's very easy to administrate and has a great web-based GUI. Apache is fine, but it's a bit more complicated to work with.
NOTE: I just noticed that Moodle is available from the Cherokee-Market, meaning you can deploy it using Cherokee's GUI. http://cherokee-market.com/#7-Moodle