Unlikely, the engine won't run at all without a cam sensor signal. How are you sure that the VSS is working?

You don't absolutely need a scanner with OBD-1 Mopar EFI ('91-'95). The codes can be read by cycling the key to the run position from the off position three times, leaving the key on the last time. Then you count the check engine light flashes to get the codes. There will be two digits. It will flash the first digit, then pause, then flash the second. If there are more than one code stored, there will be a longer pause, then it will flash the next code. All the codes will be two digits. You will always have a code 55, it is normal when the PCM is working.

If you don't have a check engine light connected, find the wire from the XJ PCM harness that used to operate the stock check engine light, it is a thin black wire with a pink stripe. Connect a low watt test light to the wire on one end, and the other to the battery positive. The test light will act as your Check Engine light temporarily.