The trouble is, as long as the walkie talkie is transmitting, it can't receive. You could key it with a VOX (voice-operated relay) circuit. You would lose the first syllable of the first word, then you would have to wait for it to stop keying before you could reply. The squelch circuit of the walkie talkie would have to be wired to key the intercom when it received a signal.
It would be easier, and probably cheaper, just to buy another wallkie talkie and have the person use that instead of the intercom.