It's possible for sure, but do remember that the further away the MySQL bit of the server is from your web server, the slower the connection is likely to be. If the two are in different data centres then you're adding even more slowdown.

Speeding up the above setup with Amazon - best way I think would be using something like memcached to cache the MySQL queries on the web server where possible, and if possible use other web server caching too especially if the pages aren't changing on a regular basis.

Do prepare for slowdowns with this however, possibly much larger than running MySQL and Apache on the same busy server.