No. And the way you're wrong about this is important. Any plain whole milk yogurt thickened or stabilized with starches or pectin is a UPF; Kroger's Plain Whole Milk, for instance, is a UPF and it isn't sweetened.

(For what it's worth, I really dislike yogurt and would not in 1000 years consume a sweetened yogurt product, though I do work skyr into every other meal these days for protein-maxxing reasons).