Will there be a time when units can be promoted to receive stats such as increased damage and health due to fighting other units over time and such?
These are a confirmed no. Units don't survive long enough, and there's way too many units for this to be worth adding. Unit promotions promotes micro and this game is focused on macro. You should check out the confirmed features list which is linked to in the FAQ and the Useful Threads post.
I would like to add that veterancy goes directly against What You See Is What You Get, pretty sure neutrino mentioned that it was one of the things he disliked about it (and I agree with him there).
