is it just a model change like turning bowser into dry bowser

as long the movesets isn't altered at all it's fine i think?

as long as the mods only change the visuals on your end, there should be no issues. but if you change the physics, it will cause a desync on both systems causing the game to go "wait a minute, somethings not right" and proceed to give an error due to how its coded

If a character is only modded on your end it's absolutely fine. If there's something like a custom character, or modified moveset it'll be impossible to use online anyway (you'll just get instantly kicked off)