Would an unpaid gym bill affect my credit.. ?

Hey bizarre question but i was living in Dresden , Germany for about two months, apparently I was on a contract but I contacted this gym notifying them I was leaving and also asking to cancel my account. She said she was sorry to hear and that it would be done within 2-3 days. When i returned i had a 200 bill telling me it was being to collections. I was upset and called to speak with "Kip" the manager, he said he had no record of me canceling my account and that I owe them 200 dollars. I told him I was not going to pay him. Can a small bill such as that affect my credit considering I didn't give my social security number when registering? I have no other credit cards and am 19.