This is a bit tricky, as you say the manual is unhelpful.

Since it can be powered by AC it obviously has a built-in bridge rectifier. Conventionally the negative side of the output of this would be commoned to the metalwork of the box which would be grounded to the rest of the wiring ground. If that were the case, then you would NOT connect either side of the AC supply (from a transformer) to earth because if you did the rectifier diodes would be short circuited across the supply on one half cycle or another and would have a short if merry life! A/k/a a loud brown smell (guess how I know?). If you kept the AC supply isolated there would be no problem.

With a DC supply, and if one side of the rectifier is connected to the driver case, then it would be OK to connect the same polarity of the supply to the case as the rectifier - one of the rectifier diodes would just not conduct as it would have a short across it.

So it all hinges on how the internal rectifier is connected. My guess is that it would have its negative output connected to the case. To check you need a DMM with a diode setting in the resistance ranges - both my DMMs have this. Assuming they are typical the positive "V/ohms" input (usually the red socket/lead) should be connected to the case, then look at the reading when you connect the other (common, black) lead to either input. (A) if the meter reads a low value (on mine ~0.6) then the negative side of the bridge is connected. If not try the leads the other way round: (B) if you see a low reading this time it's the positive side. If neither gives a reading then (C) the case is isolated from the electronics.

In cases A and C you can safely connect the case to the system ground. Case B is more difficult - do the measurement and see what you get, let us know and we can think again.