Personally, I have never minded construction. Disney generally goes out of their way to keep noise and disruption to a minimum. That said, it is possible you could hear some work during the day.
I don't really think any of us can really answer as to what level of noise would 'ruin' your personal ability to relax, because that answer is too subjective.
I can't imagine Disney ever terrorizing the animals with loud noises, if that's the level of noise you are imagining. I was once Stayed at AKL while the lobby was being refurbished. when we walked through the lobby, the work wasn't 100% silent, but I don't recall hearing much of anything from our room. Once, when we stayed at CR, the room next to use has some sort of problem that required a fan/blower, likely water damage of some kind. We could barely hear it.
In my experience, the worst WDW hotel noise pollution comes from other guests: excited children, a guest playing guitar on their balcony.
Oh, and well....most lounges have tv's that are too intrusive. A little local news, with traffic and weather is okay. Highly political cable news covering terrible tragedies, UGH! The same Disney song over and over every day, UGH! (happens often) A Disney movie, better, but still a distraction/noise we don't need. I want to be in the moment. I go to WDW to vacation. I want to think about sun and fun!