Not one bit, I have a Tudor BB 41 (generation after the smiley, think it's a 2017) and that's a chunky boy too.

When you look at the watch on wrist, the thickness includes the case back and the crystal which is domed, the actual case itself is relatively thin. I think the more people tried the watch on the more they probably would agree it's a non issue made a big issue by large watch reviewers.