My local Ford dealership told me that my battery keeps going dead because the "four wheel drive motor has burned out and keeps draining the battery. The repair $600.00? Before they replaced the battery they told me it was fine then they say it has a bad cell. Sound right to you?

Only way to test the battery is to load test and most Autozone stores will do it for you on the car in hopes you will buy one at their store if it is bad.
Now for the 4 wheel drive motor... the only 4 wheel drive motor on any vehicle I ever heard of is the same one that runs your vehicle itself. Most 4 wheel drives (I ever heard of) have the motor, transmission and transfer case. All pretty basic in all vehicles and the 4 wheel drive is engaged either mechanically with a lever, hydraulically with a button/switch or in some cases by vacuum. At the end of the actuator regardless of which type of activation to my knowledge there is not a separate motor. You could have an indicator light that stays on but that is about all I know about that and all I could find looking through a Chiltons Manual for Ford trucks.
So to answer your question... No it does not sound right on the 4 wheel drive motor. THe battery.. It is possible that when they checked it it was good. Then a few days/weeks later it goes bad. That is very possible. That kind of thing happens. My best guess is you do not trust them and if that is the case you should try somewhere else before doing the repair they say is needed.