First, I'm not sure what it is that you are referring to that you want to connect to an external earth ground point. Are you talking about grounding the chassis of the equipment, which would normally be grounded anyway via the AC safety ground pin of the power plugs (assuming they are 3-prong plugs)? Or are you talking about connecting the signal grounds/circuit grounds of the system to earth ground?
In either case, though, I agree with Ralph/Atmasphere that if your equipment is properly designed you are unlikely to be accomplishing anything constructive by adding extraneous ground connections. In addition, you would probably be introducing a code violation, and possibly serious safety hazards as well. See the upper part of page 8 of
this paper.
Regards,
-- Al