I run my Bantam coolant pump from the same VFD as the main motor. As long as you are running somewhere close to the nominal speed, like within +/- 50%, it operates OK. The flow obviously varies with the spindle speed but you can adjust it with the tap.
Generally speaking, if you are using coolant it probably means you are using some power in which case you should be in roughly the right gear and your motor should then be operating reasonably close to nominal.
As pointed out, the impeller is symmetrical, so it works equally well in either direction. At one point I had to dismantle the pump to free it up but otherwise it's pretty simple and looks almost bullet proof.
Murray