The RTS games I know definitely do collision detection. StarCraft 2 disables collision detection in a few cases: workers harvesting resources, adept shading, and the colossus walking over ground units. To see what no collision detection would look like, see how the air units stack and move across each other.

I think collision avoidance might be overkill. It's fine if two units bump into each other while going in the same direction. Collision is bad if some units are moving through a choke point and the units in back turn around to take a different route because there's no open grid squares to walk forward through.

I'm currently playing through the StarCraft 1 campaign and the pathing differences with 2 are huge. Imagine being in line at Disneyland and every ten seconds, the people in front of you decide the entrance is blocked and turn around to try finding another way in. Then they bump into you and turn around again. Or maybe they just keep bumping into you for a bit.

I wrote a paper on this a number of years ago. Here were my primary sources:

https://arxiv.org/abs/cs/0007021

https://arxiv.org/abs/1203.1895

I believe the second depends on the first.