Hello again Sean, If the compressor runs in cooling mode, without the outside fan running... the compressor can be ruined. I would not take the chance myself.
Having said that, the compressor will go *off * if it is allowed to run without the outside fan, its controls are wired through a high pressure cut out switch... the compressor will only run a few seconds if the fan goes off in AC mode.
Pay close attention to this last paragraph I have typed above.
It could be that your comment that the outside unit was getting real hot was due to the sun shinning on the sheet metal, and that the fan had actually not quit as we both had assumed... **but the the entire outside unit was off. ! That sheet metal can easily get so hot that you can't hold your hand on it.
If thats the case, then resetting the system by cycling the power at the air handler would work if the outside had gone off on its high or low pressure cut out switch.
A dirty outside condenser
coil will cause the unit to go off on its high pressure cut out switch... if the unit is over a few years old. .. and its been going off in hot weather, then the condenser coil should be cleaned.
**A totally clogged condenser coil can look clean ** the dirt embeds deep between the fins where you cant see it. The way to clean the condenser coil is to *blast* water, forcefully between the fins of the coil unit you see water coming out the back side of the coil by looking down through the fan. A good job takes about half an hour.
Do the job with power off to the outside unit, and don't get any of the electricals wet.
Let me know if that makes any sense on your end or not, we can go from there.