And just how powerful a Green Lantern would he/she be?
Or would the Guardians, or the Power Ring reject a Kryptonian because of all the additional powers the combination would incur?
You pretty much answered your own question. We know a Daxamite that 's been chosen, and clearly the powers that be had no problem with that.
And since we know that race is in power equal to Kryptonians I don't see what logical reasons there would be to exclude them.
The only real difference between them is one race has a weakness to lead, one has a weakness to kryptonite.
Are both equal vulnerable to magic?