I'm sure a rim could be weakened in this way, but I don't know how the damage would present itself.

In my experience, rims fail in various, but predictable, ways:

--catastrophic failure; a severe impact twists the rim or otherwise breaks it so badly that it cannot be ridden or fixed. Obviously you would need a new rim and spokes immediately.

--permanent damage; less severe impacts put dents or flat spots into the wheel, or knock the wheel badly out of true; it can be pulled back into true, but spoke tension will be uneven; spokes will soon start breaking and eventually the rim will crack around the holes. You might be able to ride for quite a while, but you will need a new rim, and probably spokes. How soon? Well, better sooner than later, but rims can be surprisingly resilient. My wife rode for several years on a wheel that had been totally taco'd. I'm sure the rim was permanently weakened, but I got it true again, and it was still true when she sold the bike (don't worry, I told the buyer!).

--brake surface wear; this takes a long time to become a problem, but eventually the walls become so thin that they cannot hold on a tire; they crack. Once this happens, you may be able to ride for a little while, with lower tire pressure, but have to replace the rim as soon as possible.