Does an EMP grenade do damage to anything other than equipment?

EMP grenades do not do damage to enemies (as in potentially lethal damage which turns their screen red), though it will register as a "hit" on your reticle and cause a very brief stun and weapon jump.

As far as the EMP effect itself, it will affect their HUD as normal EMP killstreaks do (disable radar, red dot sight, and ability to deploy killstreak rewards) for a few seconds.