Yes..............and no, lol.
Back in the late '80's Ford(and the others) started using electronically controlled Automatics, since they already had an on-board fuel injection computer(PCM) they added the trans control software/firmware to that.
So..............the Explorer PCM will "look for" the automatic trans connections, which, of course, won't be there so it will turn on the CEL, PCM will still run the engine OK, may get some high idles now and then, not sure on that.
If you can find someone with a programmer for Ford PCMs they can change the software to manual trans, guessing it would be $200-$250, they could also delete the PATS check if so desired.
I think 1996 was the last year F-150 came with 5.0l and first year of new PCM(EEC-V), if you could find the PCM from a '96 F-150 2WD 5.0l manual it should works as well, and no PATS that year.