In short, yes. You’re cascading one boost into another (distorting a distorted signal) and also driving the front of the amp harder. In addition, Tube Screamers are very mid centric and whilst often sounding great in front of a clean Fender style amp, adding them to an amp with more mids (typical Marshall type voicing) you’re getting a rather large hump, mid range in your EQ, which adds to that harshness you’re hearing.
Rhett Shull recently did a video on TS boxes.