I think the answer is yes, but I'm not a skilled enough mathematician to give you a great answer... The little bit of information I found online says that a standard size party balloon weighs about 0.14oz, and takes a little more than a pound of pressure to pop a very full balloon, so presumably it would take at the very least the weight of 114 balloons all pressing down on one balloon to come close to popping it. So if you had a very tall and very narrow enclosure where there are only a few balloons on the bottom layer then they would probably pop under the weight of just a few thousand balloons.

So the short answer is yes, but for a definitive answer you would need to know how fully each balloon is inflated, the thickness of the balloons, how many are on the bottom layer, what the ambient air pressure in the room is, the temperature, are you above or below sea level etc.

Once you had all that information you would then need to give it to someone better at math than I am to figure out lol