RC Compatibility

No. Cannot connect it to the Inspire RC.

I'm curious as to what the differences are between them? I'm in the same boat as the OP.

The P4 uses a GL300C and I think the P3 used a GL300B but difference were in the switches and battery I think. Don't know the RC model of the Inspire 1, and I think the new Inspire 2 may use dual GHz frequencies that preclude using the P4 RC. Dunno.
 
GL658A B and C are the 3 models that can be used with Inspires. I don't remember what the exact difference is. This has been asked several times on the DJI forum and DJI moderators chimed in with a reason. I can't find the threads now, but I know it is not possible. It has to do with the frequency that the master connects to the slave with.
 
Inspire 1 radios work with Phantom 3 and 4 aircraft...lacking in 5.8ghz, the P3 and P4 controller will not work with the Inspire 1
 
Can a inspire remote be bound to a I1 and P3 at the same time?
I owned a P3 and I1 at the same time and as the I1 controller had HDMI out I would bind it to the P3. I constantly had to rebind back and forth so I would say based on encryption...1 controller does not rule all.