VFDs dump more watts into the core due to harmonic losses, so you will have to pay attention to that if you are running that motor near its thermal limit.
i don't machine much aluminum, mostly steel so i'm running below 1/4th hp at the rigidity limit of the machine.
As long as you program the vfd to deliver 2 volts per hz (120vac at 60hz) then you won't have any problems.
If you want to run that motor well above 120vac 60hz then you might back off just a bit on the voltage. 1.8 volts per hz perhaps.
if you want to get really creative, that is a capacitor run motor. meaning it has a second winding in series with a capacitor.
if you remove the capacitor and connect the second winding to one of the other phases of the VFD you should have direction control, and it might perform better..
you might end up burning it out however.
if you have an ac amp meter i would clip it around the capacitor during normal operation.
if you run into very high or very low amps through that capacitor when running the VFD well above or well below 60 hz (keeping 2 volts per hz) then i would attempt to fix this problem either by increasing or decreasing the volts per hz for that part of the curve. (you should have several options available in the vfd)
as far as i know the amps through the capacitor should approximately equal the amps running through the other winding.
but if you only intend to run it at stock speed, just set and forget the VFD to output 2 volts per hz.