Very unlikely.

First, how can Joe know that the nuclear power plant is OK just because it didn't explode? Modern nuclear power plants are designed to safely contain the reactor core in case of an accident. So even in case of a complete reactor meltdown, the facility might look perfectly fine from the outside. He might not notice until he breaks a door open and is greeted by several Sievert of deadly radiation.

But let's assume that the facility actually is safe.

I am not a nuclear technician, but I am quite sure that starting a nuclear power plant requires more than just pressing the "On" button. However, chances are good that Joe will find the manual in a cabinet in the control room and can use it to teach himself the procedure to start the reactor.

But the problem is that the reactor likely did not shut down properly. When the apocalypse happened, then the reactor likely shut down automatically because some safety system was triggered. That means the facility is now in a failure state. Trying to get the facility out of that state might require some manual intervention. Trying to do this without the advise of a trained technician will likely cause more damage than good and might ruin the power plant once and for all.

Even with a technician the facility will require offsite power to start up. Nuclear power plants also require offsite power to keep running. Loss of offsite power is a critical failure event which will cause an immediate shutdown. After the powerplant was started it might be possible to rig it to ignore a LOOP condition, but again, this will require a trained technician who knows what he is doing. And then it comes to maintenance of the plant. Sooner or later Joe will have to get some new fuel elements (if he is lucky, there might be some in stock) and replace the old ones. I am quite sure Joe will certainly not be willing to get anywhere near these, unless he is willing to sacrifice his life for the community. Actually, unused UOX elements are safer to handle than one would assume. They are toxic, but only lightly radioactive (but Joe might not be aware of that). The used ones, tough, not so much.