Good Day,
I have been using AWS quite a bit for my cloud based system for a hardware project. Using SimpleDB and the notification service provided is great.
Short answer: yes.
EC2 instances are just like any other virtual machine, obviously you can put in a server that listens to UDP. Configuring the network for this is, of course, slightly more complicated, but possible. The one thing making it more complicated is that with UDP you will not be able to enjoy the load balancer service that Amazon offers, as it (currently) only supports TCP-based protocols.
So, if you have one server you wish to put on the internet, the procedure is probably same as what you'd do with a TCP server: set up a server and an elastic IP pointing to it, and then have your clients connect to it (by knowing the elastic IP you've been allocated, or by referring to that IP via a DNS resolution). If you have multiple servers you wish to set up, answering the same address, life is a bit more complicated. With TCP, you could have set up an Amazon load balancer and assign your elastic IP to the load balancer. If you'd want a load balancer for UDP, the Amazon stock load balancer can't do that, but you can still find a software load balancer (there are hundreds of them on Amazon's public images library) to set up.