I can buy that. I'm cool with physics bending tech. To be honest I don't think mankind will leave the solar system and in fact, I think Mars is as far as a human will go because there is nothing else worth landing on that is a distance that we can practically reach, so sci fi has to break the rules to be interesting. And I don't see generation ships ever being something humans could agree upon.
While I was being a bit silly, I don't entirely mind it either, so long as it adheres to its own rules, and this is a case where it also makes me scratch my head a bit. The thing they used, from what I read, is some array the Geth jury-rigged from three mass relays, but I thought the mass relays could only ever connect to one another. Seems odd that the geth could somehow manage to do it, though I guess if any race in the current galaxy could fiddle with reaper tech successfully, it'd be the geth.
Still, the info about the whole initiative is too shady to me and story-wise I expect some twists, including Cerberus, to rear its head (especially since one of your teammates shares the same last name as the Illusive Man).