Not necessarily, a lot of people choose a club and stay with it for various reasons. When you choose to support a club you start to feel a connection to the club and what it stands for regardless of whether or not you have connections to the city the club is from. If you really liked a club why throw away years of support when they're going through a rough patch? Like for me in EPL football, I am a Liverpool fan and the club right now is quite frankly a joke, but I'm not going to up and leave and support Chelsea or United or City just because they are more successful at the moment, or because I'm not from Liverpool and feel I'm not obligated to stick around. Same with Barca in La Liga and when the inevitable time comes that they will no longer be successful. It's not "being too obsessed", it's called not being a flaky fan.
For people like you though who seem to be more of a fan of beautiful football than being club-loyal (and admit it), I don't think that the term glory hunter should be used toward you. Because like I said people enjoy football in different ways, it's only "bad" if they obsess and put on the image of being club-loyal but aren't. At least to me anyway.