If it is obd2 then it should work not matter what code reader it is.
Our trucks are Not, strictly, OBD-II (despite the connector) and a generic
OBD-II is pretty much useless for us
You need a professional scanner (Mac, Snap-On, Ford, etc.) or, what most here use, the AutoEngunity diagnostic tool with the Ford Enhanced Package.
That being said, although it won't read the most useful Ford diesel codes, a generic OBD-II code reader should
at least connect and pull some of the generic codes (typically we see people saying "My SES light is ON but I have no codes"
when using one of them)
So, I think you have another issue with it too. There may be a fuse to the OBD-II port that's blown (see if you have power in the cig ltr (outlet).
If the PCM was dead it wouldn't start at all so, I think it's running OK.
The first test I would think of its to unplug the ICP sensor to see if, by having it default to a "limp" setting, if your idle stopped the wandering that would be the clue. Also look for fresh oil in the connector indicating the seals are failing and it needs to be replaced.
Next, I'd throw-in your spare CPS, if you have one, and give it a try. If you don't have a spare, I'd be a good time to get one to try