Yes, they'll send you to collections. The collections company will take their word that the debt is valid and try to contact you. Until you pay them, they will report the debt on your credit. If you manage to convince them the debt is invalid, you will still have to separately convince all three credit agencies to remove the listing. Comcast's large bureaucratic collections department will just send you to a different collections agency until you pay up. You can then get a lawyer to stop them, but comcast won't just back down. They'll reply to the lawsuit until a judgement is given. This will cost thousands of dollars to complete.

The other alternative is to play their game with their customer service and get them to agree to properly cancel the service.