zerg verses the federation

[starcraft]

timefraime a month before the end of the dominion war
after the second zerg mission the entire swarm left tarsonis to go to char then Insert technobablle the zerg swarm including the chrysalis and are now in the star treck galaxy well say the star treck galaxy has gas and minerals they just don't use them. and naturaly decide to invade the alpha quadrant
more specifaly how will things be different will the dominion take over the alpha quadrant also the zerg have a type of wormhole drive and without it let's just say that youre speed is about 1,000 light years a year you invade also the entire swarm is at least 2,000,000,000