It depends. The approach of courts to non-compete agreement clauses varies greatly from state to state. Some states are very eager to enforce covenants not to compete and will actively rewrite those which are too broad in geography or time to make them more readily enforceable. Other state courts have taken a very negative view of covenants not to compete and have enforced only those which very clearly were reasonable in geography and in time and which are supported by substantial consideration (the payment of money in return for the agreement.) This approach varies state to state and often depends on the facts of the individual case.
For example in Florida the law supports non-competes, so the facts of your situation, and the state you live in determine where the agreement will be enforced against you.