How would a ring oscillator with even number of inverters behave?
It likely wouldn't do anything interesting. 

With an even number of inverters, there should be phase shift through the ring of 0 degrees, but there is no DC inversion at the end of the chain, meaning the circuit should be inherently stable.

Initially you may find that they start up in an unstable state but at some point it will settle down because there will always be one inverter that is slightly stronger than the rest - usually the output node as it would normally be loaded.