The Immortals have obviously been around for a lot of troubled times in humanity's history. As has The Doctor. They have definitely met, probably multiple times, and spanning multiple regenerations.

The Doctor has most definitely figured out that they are immortal. Have they figured out that it's the same Doctor they keep meeting? Do they know about aliens? Have they been in the Tardis? Perhaps one of them was a companion for a brief period?

I really don't care what you do with it, I just think it could be fun crossovers.