Never thought about it, but yes, probably.

Either that, or the quality of the noise reduction reduces. Imagine again playing a sound with throughs where the original sound had peaks and visa versa, but with a smaller magnitude than the original sound. Now the magnitude of the resulting wave will still be reduced, but not become exactly 0, so the noise cancellation will be imperfect

In particularly hectic environments, my AP Pros struggle to really block a lot of noise, mostly just voices and car sounds, but larger noises still make it through the headphone itself, bypassing the mic (but also hitting the mic, so you get some amount of ANC on it) and hitting your ear.

I think this would be a similar question to asking "do my headphones die faster if I listen to things louder", which I don't think is a big enough effect to worry people, I've never heard of it anyways. There's pretty much never not sound. Surely headphones have a lower level of reception or tolerance where it doesn't bother or can't pick up those noises, but it would always need to be listening and ready to generate them, so whether it does and how much it does seems like it'd be the smaller part of the process