2005 Hyundai Elantra Check Engine Light

My mom recently took the car in for oil change and the mechanic told her to change the air filter. I told her I could do that on my own and wasnt worth 20 bucks. A week or so later the light came on for check engine so I took my car to autozone and they hooked up the tester and told me an emmisisions leak was the problem. My question to you is.
Can a cut in the air filter rubber foam seal cause this light to come on? I have replaced the air filter and noticed 2 unusual cuts in the old one. Prob the mechanic trying to make a few bucks. The autozone person told me to drive it for a week and see if the light goes out. Is the air filter cut a possible engine light problem? Thanks
tim
las vegas, nv