A couple of considerations:
1) Don't Control Logix processors talk to each other over any number of digital protocols?
2) To have parallel resistances come into play, one would typically convert the 4-20mA current signal to a voltage, and then transmit a voltage signal to the second PLC. The 4-20ma is converted to a voltage at an input anyhow, the CLX uses 250 ohms as a dropping resistance (pg 20, Installation instructions, 1756-IF8H).
So, the 'first' PLC uses 250 ohms on its input to convert the current locally to a 1-5 Vdc signal, the signal across PLC 1's input then is wired in parallel to the 2nd PLC, which has > 1 M? input resistance for voltage signals.
So, doing it that way, no, the parallel resistances are not a problem: 1M in parallel with 250 ohms.
2) Or you could send 4-20mA to both devices, since the 4-20mA is a current signal, the 4-20 wired in series to each device: source + to input 1 +, input 1 (-) to input 2 +, input 2 (-) to source (-).
Either method could be problematic if the 4-20mA signal has HART superimposed on it, and the application intends to use HART for either configuration or for its ability to carry diagnostics or multiple variables, then you need to make sure to confirm whether or not the analog input would 'strip off' the HART before it gets to the 2nd input.
If the 4-20ma signal is an active output, powered internally from whatever it is, try to ascertain whether the output is isolated or not. Signals that are ground to the source device can be problematic when connecting to multiple inputs.
3) The I/O manufacturers make DIN rail mount boxes that will duplicate a current signal, one current in, two current signals out, some people call them splitters.
Dan