I doubt that "ops normal" can be considered restricted to military use. In the 60's when operating an HF Oceanic communications position all aircraft were expected to give an "ops normal" every 30 minutes, as far as I know it really only meant that everything was going according to plan.
For any ground station to ask "are you OK" in this way seems very odd to me. In the few instances when I have had a concern for an aircraft at take off I have either kept quiet or stated my observation. The former occured when an aircraft departed in a very strange attitude and never climbed out of ground effect (DH89a when cargo has slipped to the rear) and the latter when I saw vapour trailing from a DHC6 (fuel leak or fuel cap, cant recall exactly).