Avoiding RCD tripping with Inverter Drive
Although dangerous, hypothetically, would removing the Earth
  connection from the drive solve the problem? In doing so, there would
  be no current leakage down to Earth.


The possible (or even likely) cause of the RCD tripping are common-mode EMI filter capacitors on the supply AC input inside the inverter drive. Given that they connect both live and neutral to earth, the capacitance on the live side is going to create a bigger earth current than the ones on neutral. This creates an imbalance current and could cause an RCD or GFCI trip.

Of course, there could be other currents to earth that "get there" not via the incoming earth wire but by some other leakage mechanism and so, removing the earth wire might not hypothetically "solve the problem".

But it would be dangerous to do. Consider this: -



C1 and C2 are the common-mode EMI reduction capacitors referred to above and, as can be seen they might connect to the case of the inverter as well as the incoming earth wire. If that earth wire is removed and the case isn't earthed by some other connection, then the case will attain an AC voltage that is 50% of the incoming AC voltage due to C1 and C2 acting as a potential divider. If those capacitors are 10 nF each you would get a nasty belt when touching the case.