Not so much for the booster. There’s typically a high ratio between first-stage mass and payload. Maybe 10:1 in the usual case, though probably a bit less for a return-to-launch-site booster (say 5:1).
The ullage gas itself has significant mass at MECO. Considering just the booster alone, there’s probably at least 2400 m^3 of volume for LOX, which at 6 bar and 500 K is ~11 tons. That could shoot up far higher if it got chilled due to slosh. Can’t be ignored.
Some speculation is in agreement with that idea:
Will the secondary dome have some extra protection? Heat tiles, or maybe just made from niobium? We shall see.