Yes, the glass's sides are still full of the disgusting soapwater from the bucket that's now basically 95% other people's drink dregs.
From a health perspective, I'd be more worried about the leftover sanitizer in the water in the glass. Bleach is pretty common, and it's honestly a tossup whether I'd rather drink someone else's dregs or bleach. It's probably the dregs, I'll take a stomach flu over melting my stomach lining with chronic low-grade bleach exposure.