I'm one of the original RTEMS developers and been the RTEMS Project lead since it transitioned from an Army research program to a traditional free software project.
We try very hard to keep RTEMS as a high quality product with a great community.
The AVR is a quite small target and the RTEMS port is incomplete. Even if the RTEMS port were complete, I do not think there is an AVR with enough address space to support GNAT/RTEMS. GNAT maps each Ada task to a POSIX thread just as on GNU/Linux and the run-time footprint for a "real Ada" environment is large. I recall minimum executables in the 400K code range on a PowerPC. In comparison, the RTEMS minimum C executable is probably in the 32-40k range on that same target.
I am not that familiar with AVR-Ada but I would agree that it is highly unlikely to give you a full Ada environment.
The RTEMS Project has scripts which we use to build the GNU tools and test them. If you are interested in building tools for your own odd target, they can be a good guide. The procedure doesn't vary a lot for embedded targets.
Marc C.. since you are in Huntsville, we will have to get together for lunch sometimes. Our office is roughly across from Bridge Street. I really don't get to meet many RTEMS users. :(