The coolant pump only uses a fraction of the power the spindle will use, so I personally wouldn't say it's going to be a major issue in terms of doing anything bad to the VFD, especially considering the coolant pump isn't likely to be running near it's rated power.
However, what if you want to use the VFD to change the speed of the spindle?

Other option is a simple static phase converter using a capacitor to power the coolant pump.