Yes in theory it's possible, there are two biggest hurdles really. One is discovering a way of FTL travel or some sort of suitable hyperspace alternative, but that requires some sort of energy generator that is currently well beyond our comprehension as it requires near-infinite power. There is also the 'Great Filter' to overcome as well, although we don't know yet if we have passed it or if we simply haven't come across it yet. (http://en.wikipedia.org/wiki/Great_Filter) But if we did crack that, then we've already discovered a whole host of 'earth like' planets we could potentially expand into, and humanity is extremely good at breeding and spreading. Whether that's good or bad is a very philosophical question. I think we'd need to have some sort of realization that we need to function as a collective whole, like WWIII and first contact did for humanity in the ST universe. Honestly I think the Mass Effect universe is more likely then Star Trek, less of a utopia. If there was a Starfleet though? Good grief no, space is dangerous! I'm a total coward.