I need a question answered that I have put alot of thought into and the only reasonalbe answer I can come up with is Yes... So here is my question

The school I work at has a WiFi connection and we have people in and out of our school all of the time with there laptops. I was wondering if that persons laptop is infected with a virus and attaches to our wifi does that mean that they can infect the rest of the school. We have fairly good av software however once and awhile a virus does sneak by.