At the risk of getting my head bitten off.... it's not super dangerous to run a spindle without ground being connected. That doesn't mean it is advisable though. It has the potential to be dangerous if there is a problem with the VFD.
I briefly tested my spindle without a ground connection before I installed the newer style outlets (which all have ground now). It worked fine. It wasn't that long ago that two pin outlets (with no ground) were the norm and within code in America. One of the vendors for Chinese VFDs and spindles has a YouTube video where they state that ground is optional.
A ground connection is a safety feature to prevent you getting shocked in the event there is a problem with your VFD. So.., if all else is well, it should never need to be used. I don't have that level of trust in Chinese VFDs though.... plus you might have an issue with your wiring...
Given the voltages involved and the potential consequences of a problem, however unlikely, it would be stupid not to connect to ground where a ground connection is available. It cost me less than $20 to install a new grounded 50amp 240v outlet. Surely it is better to fix the wiring problem instead of skipping a ground wire....
I found that the screw terminals on my Huanyang VFD to be far too close togeather for the gauge of wire needed for my spindle. I was worried about a short from a stray bit of copper wire etc so, I individually wrapped the ends of each cable with electrical tape and copper EMI shielding tape (so there is no unshielded part at the ends of the cable and no possibility of unwanted wire contact. It works very well.