The Alliance themselves wouldn't be tasked with the sole responsibility of earths defense. Each individual nation would still need to keep and maintain their own terrestrial armed forces.
If I recall, the codex says that the Alliance is comprised of about a little over 2 million personnel. That's roughly the same size as the U.S's armed forces today. Fighting a war on two fronts (Afghanistan and Iraq), that had our combined forces stretched dangerously thin until more recently. And those two wars took place within the same general region of the world.
Had we been invaded by say, N. Korea, it would've taken roughly a week to withdraw our main fighting forces back to the states to reinforce the defenses. Now imagine stretching that same force out across half the known galaxy, and you can see the sheer logistical nightmare it would be trying to rally everyone back to earth.
Granted, the Alliance would've pulled as many ships and personnel back to earth right after Shepard's little "oops" to be ready for a possible war with the Batarians. But they would still need to maintaine patrols and garrisoned troops around their colonies to repel any possible pirates/slavers who would most certainly have taken advantage of the situation with their absence. And with the amount of space to be covered in the traverse, it's likely that the Alliance would have 1/3 or less of their entire forces stationed at earth.
So continuing the trend of assuming they're using real world logistics (to a degree), and that space travel seems to be about as common as international flights here on earth if not more so, the probability is high that each developed nation has their own fleet of commercial space ships and an "FAA" to govern the whole mess. It's also highly probable that, just like our FAA, they would have a contingency plan to try and evacuate as many people as possible during very specific circumstances, and I would assume an alien invasion could be part of that plan.
But even with all that, less than 1% (way less) would be evacuated off earth during the reaper invasion. Many would only be able to just run to the hills, so to speak and try to survive in hard to access remote locations (a jungle or rain forrest would work wonders), and the majority of the ground fighting would fall directly under the armed forces of each nation.