Can you run earth ground thru conduit into home?
All A/V equipment should be grounded at the main disconnect via a intersystem bonding terminal block attached usually to the grounding electrode wire right below the main disconnect.

Unless your detached garage has it's own main disconnect, which you'd know what to do by the above paragraph, then you are really only bonding the coax at that stage which is probably not hurting anything unless the detached garage is not grounded/bonded properly itself.

Intersystem Bonding Terminal