if I'm wearing a button up shirt under a blazer, I definitely tuck.
In fact, I even tuck my t-shirts these days.
It's very difficult to make a button-up shirt under a blazer casual and SW&D. That's why a tee is a much easier choice. I've seen a few synthese fits where the shirt was untucked and it looked good.
What I'm thinking of doing is getting some mandarin collar shirts