Usually, when the ABS module fails, the vehicle will still stop altho you will not have the ABS function. In other words, in everything but a panic stop on a wet road, your brakes will feel fine.
I am not sure why the ABS module affects the way your engine runs or the transmission shifts. Perhaps you have a vacuum line that has come loose/failed and that is causing an entirely separate problem from the ABS warning light.
I am not saying that the Ford tech is wrong but I have seen too many instances where they prefer to just throw parts at a problem until something eventually fixes the problem. Naturally all of this is at your expense. A bad ABS wheel speed sensor($15 part) will also give you an ABS warning light and is an easy fix. The same goes for a failed master cylinder, which is a $100 part.
If you have CoachNet ERS I would call and ask to speak to a tech to try to get another opinion. The other option is to try another garage.