Though the idea has merit, I'm not entirely comfortable with the long term implications of it. As we know them, the aliens are the enemy. They are horrible evil things that you dedicate your entire time to utterly destroying. If there was a way to somehow turn them around and make friends with them, chances are it would turn the focus of the war. Suddenly humans would not have fight for their lives but instead peace would be in grasp. You'd probably get all sorts of new age movements and organizations that claim that 'Aliens are people too' and you'd lose funding from democratic nations that suddenly decide the war is unethical because the poor aliens are just 'sick.'
Aside from that it's also like a wolf hunter using a wolf to hunt other wolves, or a Dragon-slayer riding a dragon into battle, or a communist fighting alongside a capitalist. Sure, it happens but it's a still a bit...
I feel UFO: Alien Invasion goes to great lengths to maintain some semblance of stylized realism in its interpretation of the setting. You can for instance see indications of this in the detail of the various UFOpedia entries. They appear to follow this sort of approach: "
If aliens were to come to earth", "
If this technology existed", "
if this random thing was possible" - then
this would be the outcome! I think suddenly recruiting aliens would betray that approach to realism, because in the event that it was a possibility it would theoretically change the game's objectives radically.