Hate to tell you this, but if it is a late model bike all the radio diagnostics could be done by the dealer. All one would need is the ability to read, as all the flowcharts are in the FM.
All the radio software can be diagnosed by entering the different diagnostic groups on the radio itself (as well as the CB set up mode) and read out on the display, and the hardware can be diagnosed using a breakout box.
Simply sending the radio out may or may not correct the problem, for the simple reason that you don't know that the radio is the problem.
From your description it sounds like you have no modulation. The three logical first steps are to check the electrical condition of the CB antenna with an Ohmmeter, check the SWR and substitute the microphone with a known good unit.
The way I look at it no one would expect a dealer tech to repair a radio once it has accurately been diagnosed as a internal radio problem, but until that time it is a problem with the bike and one would certainly expect dealer techs to know something about the bike.
Is this under some form of warranty perhaps?
The thing is that one could never expect a local CB shop to diagnose it without the ETFM and I would feel rather nervous having them remove the fairing anyway. If you have no leverage with the dealer you can't really force them to work on it other then on their terms, and the preferred option might be to try and find a dealer that actually wants to work on your bike, but that's up to you.