Usually, protests are located in one somewhat easily defined area, until you cannot be there anymore or the goal has moved somewhere else. So then you need to get to another spot, this is the moment you disconnect your battery until you've arrived at the other place.

So yeah, they'd be able to say that "person A was at location B and later C", but not necessarily the way there or after/before those specific locations.

I agree that the safest is to assume they can definitely track you no matter what protocol/antenna you use, so you have to chose what moment it's OK to be tracked (like large groups).