How to determine whether two ICs can be clocked from the same source
You can verify the internal outputs when driving both inputs.

The two pins are just an unbuffered inverter (1 stage) with a 10MOhm or so feedback resistor that a crystal or ceramic resonator Pi filter with 180 deg phase shift can resonant with enough gain (>=10) to create a square wave out.  The Resistor feedback inside self biases to Vcc/2 to create 50% duty cycle.

When you drive the CLK input externally , the internal feedback (is shunted by your active clock and) has no effect.