In general it would not be advisable to tie the DC bus to earth ground, because the AC line may also be referenced to earth. Having two competing ground references in the same circuit can cause substantial issues. I suspect the rectifier diodes would fail rapidly, if a fuse didn't save them first.
But suppose I wanted to power the drive through the DC bus terminals. In this configuration, the AC terminals are left open, meaning there is no competing ground reference. The VFD and motor chassis are tied to earth, which can lead to common mode issues, but I don't see that they'd be any worse than running from an earth-referenced AC line.
In that configuration, would there be any problem with tying the negative DC bus to earth? Is it possible to make a general statement, or would it be installation- and equipment-dependent.