This is probably a stupidly insane question, however should the CNC machine be strapped to earth?

If everything is connected correctly it should have any earthing it requires, adding earth straps randomly can cure or cause problems but the answer is "It Depends" ;-) 
Details of make, model etc. might help folks form a useful opinion, my CNC mills are earthed by the 3 phase connection to the motor, the wiring shields are grounded at the controller end to it's enclosure but are not connected at the machine end,

 - Nick

It's a regular ebay-sourced 6040 with Huan Yang VFD and spindle. Up to now I've made a possibly rash assumption that the spindle case would be earthed, and with the spindle being bolted to the frame that carried the earth thru.

However I do recall viewing some discussion on online forums about earth loops, and as I have an inkling what they are about I can see valid reasons for not adding an extra possible earth loop.

An earth ground is only a safety item to prevent something from being at a different potential which could be hazardous. If it seems to 'cure' a CNC problem then you can be sure you just haven't discovered the actual problem. When I hear a CNC manufacturer recommends an earth ground it gives me very little confidence in their control.