The game does have a stalemate timer - at least in Skirmish mode, that is indeed a possibility. I don't know what happens to units left on the Strategy map if a stalemate occurs.
I was not aware that a stalemate system already existed, how exactly does it work? I've always just surrendered pretty quickly in stalemate type circumstances since I didn't think anything would happen and I didn't want to wait around for no reason.
I mainly made this post from my experience against the insane AI in skirmish mode. In many matches against them I find myself in control of the majority of the map, but unable to finish the AIs main base because they just turtle in them. The AIs as a whole just seem to turtle really hard and never mount any reasonable assaults. They seem to always keep at least half of their total supply at base at all times. They do send out lots of small assault parties and take undefended bases but that's about it.
As a result of all this I'm rarely under threat of actually losing to them directly, but they regularly put me in these stalemate type situations. In about 10 games played against the Insane AI, around 5 of them got stuck in these stalemate situations where I had no population left to make a big enough force to defeat them, but the AIs would just always leave most of their units in their base.
To be fair they probably aren't true stalemates, the AI PROBABLY could win after I lose most my forces if they mounted a proper attack instead of always leaving most their units in their base.
However I still think stalemates will be a common occurrence simply from how the game mechanics are setup, and this will be even more true after the turret buffs in the recent patch. It's just generally going to be pretty cost inefficient to take out a properly defended base, and it seems like a very likely occurrence for this to be true for both players, leading both to want to turtle.
I strongly feel like some system needs to be implemented that keeps the importance of controlling bases throughout the game, currently as soon as population pool runs out, the entire map essentially becomes pointless, all you need is to hold one main base and the rest of the map can be safely ignored. This just doesn't feel true to the design intent behind node based RTS titles.
