Short answer: In the long term there would be a major war around the time of the shift in the balance of power
It's suggested in the series there are more humans than any single species, of course there might be a larger one. Humans are supposed to be very fast at developing technology, even if we're a couple centuries behind. The yeerk technology might be too advanced to reverse engineer on it's own, like dropping a cell phone off in 1805. But there was enough data in the computers for the yeerks to reverse engineer andalite tech in a year or 2, so if any of the ships survived it shouldn't be too hard.
Given the population, and what you've already covered, humans should eventually overtake the andalites. Especially with the andalites hurting after a decades long war.
Since any major shift in the balance of power results in conflict, this mean there would eventually be a major war. Maybe not between andalites and humans, but as the andalites no longer have dominance, and humans start to take it, it's going to cause ripples in every state in the andalite's and human's spheres of influence.
This is based on that every time in human history there was a major shift in power, it resulted in wars. (which has the unfortunate implication that as the world reshapes the balance of power in the next couple decades, there will be wars).
Rainbows and butterflys right?
On the plus side, the influx of technology, new areas to colonize with ships, and since the andalite government would have been fairly well embarrassed at their plans to glass the Earth, they would give considerably latitude in human expansion, would all lead to something like a golden age for humanity, at least until we started butting heads with the powers that be.