No, you can spy on people you have no embassy with (embassies are automatically closed if you're at war, for instance). There's no negative penalty with other civs for having embassies wherever you like, and it does give a weak positive modifier with the former enemy. You don't have to subsequently accept open borders, and there's no penalty for refusing that either. So it really comes down to whether you want to cultivate good relations with that civ, or you want the options for open borders, defensive pacts or (with DoF) research agreements with that civ. If not there's not a lot of point in setting up an embassy.