I've done 5 Disney Marathon Weekends and 3 other marathons.
Marathon training in general will have a negative effect on your immune system because you're pushing your body to its limits. So, it isn't uncommon to get sick before/after.
However, I've only had it happen twice.
My first Disney Marathon (2013), I got sick the day we flew down (stomach flu) and then had a head cold throughout.
This year, I was sick starting on day 3 of vacation, sick off/on throughout, and tested positive for COVID 11 days post-Disney vacation. Not sure COVID was Disney-induced though - I have little germy kids that bring home everything from school (the one that didn't get COVID got strep throat the next week).
It's a risk wherever you might travel these days. I consider myself lucky that I avoided it for three years.