Actually, they specifically say to not run on a GFCI circuit, which is a whole different thing from a surge suppressor.
However, I know the lathe when running will actually back-feed into the power line and disrupt other electrical devices that are run off the same power circuit (For example, a LED lamp I got for extra lighting will go completely wonky and often not even work, so I ended up plugging in a surge suppressor strip and then connect the lamp into the strip.)
However a GFCI will regularly trip when you switch on the VFD as it is "seeing" a short to ground. (Due to how the VFD can back-feed through the lines)
Surge suppressors are more of a line filter to smooth out the voltages supplied (Regular household supply can vary by several volts as different stuff is being operated, and sudden surges in voltages are filtered by the surge suppressors to feed a more even voltage supply.) So I'd think it should not be a problem to plug in your VFD to a surge suppressor strip, however, I wouldn't use the typical low end strips sold for computers and the like - They are not designed to handle the higher currents, and are often notorious for overheating, melting down and causing fires. But something like a whole house suppressor installed at the electrical service drop should have no effect, and still protect against line surges (but won't do much for surges caused by nearby lightning strikes that actually can travel through the ground and back into the house, bypassing any surge suppression)
Of course, if there's an electrical engineer that knows better than I do, that cares to respond, I'll defer to what they have to say...