My furnace has a pump that collects condensation from the furnace and sends it to the same place as my washing machine water (which happens to be another pump). I'd like to get rid of the mini pump attached to the furnace by installing a floor drain and letting gravity do the work.

The only place below the slab for the drain to attach to is my sump pump pit. Next week I am ripping up part of the slab to install an interior French drain so I figure this would be a good time to install the drain by the furnace. I know how to install the drain and that I need a p-trap and proper pitch. But is it okay that I connect it to the sealed sump pump pit using non-perforated pvc?

Yes, you would use regular PVC pipe. Not really necessary to have a trap although one won't hurt. Traps are to prevent sewer gasses. You are emptying into the sump pump pit and not into the sewer line.

The reason I was thinking of a trap is because of radon. When I bought the house the basement radon reading was just below 4 units and I was told that 4 units was the action level for a basement. There is a possibility that I might have a pro install a radon mitigation system that taps into the weeping tile of my drainage system. From what I understand this would require a sealed sump pump basin (which I already have). I figured that if the basin needs to be sealed then the water in a p-trap would would help to keep the radon back... however, I could be wrong.

I see your logic. Don't know much about radon abatement but thought that a sealed top for the sump crock was used and vented to the exterior if radon gas is found. That simple.