Yes.
Once they are in a group setting/environment/school... kids get sick a lot. Until they/their system, gets used to that particular environment.
It is not only kids. I have a friend that used to work at a school. For the entire 1st year of her employment, she got sick, every single month, for that entire year. She.. had NEVER ever been so sick so often, in her entire life.
Then, once her body got acclimated to that particular school/environment and its particular 'germ' uniqueness and her body built up immunity per that school, she was sick, less often.
My son, had never gotten sick or very rarely all his life. Then once he started preschool at 4.5 years old, he has gotten sick a lot.
So did our Pediatrician's daughter, who started Preschool too.
She previously did not get sick, at all.
Now, kids are not clean people. They do not wash hands well, even if they do it at school... they rub their noses, they rub their snot everywhere, they do not sneeze into their elbow but into their hands... they put their hands EVERYWHERE and touch other kids too, they touch anything and everything. Too.
So... germs and colds, spread.
Even if the Teacher/school wipes down things everyday with disinfectant... everyday, every morning, kids come to school, again, with dirty snotty hands/noses/sneezes... and it starts all over again.