As a story, I love the DC Comics 80s run being in there, and kinda wish more tie-ins could have referenced it. But it requires the battle damage from the comics to just happen to exactly match that from TWOK etc.
Yep, here's the Enterprise pulling into Spacedock at the beginning of TSFS:not exactly, the ship in TSFS has more damage than in TWOK.
And here's the Enterprise at the end of TWOK, just before the "I feel young" scene:
Fortunately, the trip the Enterprise takes to the Great Barrier from "Where No Man Has Gone Before" in DC's Star Trek #7-8, the two-parter that occurs directly before Star Trek III, explains the extra damage nicely.