You don't say the size, but as a gross general rule, most SMALL motors rated for 230V will be OK with 208V, Baldor even has a White Paper saying that, defining "small" as 5HP and below (IIRC). But that is predicated on allowances in the motor frame for the added heat. Running on a VFD also adds heat, so I would say either/or, not both.
Instead of changing the motor, I would just get a simple buck-boost transformer ahead of the VFD and put 240V into it.
"You measure the size of the accomplishment by the obstacles you had to overcome to reach your goals" -- Booker T. Washington