Neuromarketing proved that they do not become white noise, you just stop consciously noticing them and how they affect you[1]. But even if you somehow developed some kind of immunity, you'd still be affected by ads because advertising costs are factored in product prices, when you buy something even if you never seen any of the ads for this product, you're still paying for them.

[1]: https://en.wikipedia.org/wiki/Neuromarketing#Study_examples