I would answer: No. In the U.S. there is a "lost comm" procedure which is detailed in the Airman's Information Manual 6-4-1. I this procedure, the crew should enter the lost comm code, 7600, into the transponder. If in radar range, this signals to ATC that the aircrew knows that it's radio has failed, and ATC may presume that the crew will follow normal lost communications procedures. As long as this is happening, and it looks like procedures are being followed, there is a good chance fighters will stay on the ground. If, on the other hand, The crew keys in 7500, the hijack code, I would presume chances of a scramble are significantly elevated.
Basically the procedures look like this:
- In Visual conditions, or if Visual conditions are encountered, land as soon as you can.
- In instrument conditions, do your best to follow your flight plan as it was most recently cleared.
More details are in the manual.
It is interesting that there are a few ways to re-establish communications. For example, ATC or flight service can utilize the voice feature of available navigation beacons, and may issue an instruction like, "Airline 1234, if you read, turn to heading 150." If the crew can pick this up, they may be able to respond with a turn and they can continue from there. The situation being under control, no need to send up interceptors.