Yes, youtube will give you a big scary warning about how repeated violations could mean your account is shut down. Every time this happened I went ahead and submitted counter-claim anyway. On all but one occasion the copyright claim disappeared immediately. The one exception required a bit of escalation but I still wound up on top (https://news.ycombinator.com/item?id=22488897 if you're curious).
I understand a good many people simply do not feel comfortable risking their youtube account being shut down from contested claims, but I suspect that for many the risk is a lot lower than they realize.