Travis,
Perhaps, but how did you determine that the battery is in good shape?
Remember that the battery is more likely to fail than the alternator and it's cheaper to replace. A new or nearly new battery is not a guarantee that it's good. I have had a new battery that was defective and would not start the car or even hold a charge when I got it home. I also had new Exide "Tuff One" battery go bad within 10 months.
Also be sure to check all connections for lose or corroded terminals. Then check the alternator output with a multi-meter. Often times it's only the internal voltage regulator and that can be easily replaced separately with hand tools and a little mechanical knowledge. If you decide to replace the alternator, I would look at a "Rebuilt" unit from one of the local autoparts stores. They often offer better warranties than you get from a Ford OEM replacement and they are much cheaper too. Some autopart stores will give you a lifetime warranty on their Rebuilt parts....and that's better than a new part !
...Rich