Exactly. A close-fitting white tee is just the thing; even if you're getting sweaty, it dissipates the moisture away from your armpits and stops you getting that wet patch under your arms. Now, I've never seen the point of a singlet type vest in that regard. But a tee-type undershirt is an essential for me these days.
There's another benefit too: I find it makes your shirt wrinkle less during the day, so it's not just about sweaty underarms. It keeps you looking clean and sharp too. And about two weeks' worth of pure cotton undershirts costs about the same as one pair of Marciolani socks. So why not, eh?