Can induction in parallel ungrounded cables lead to false continuity readings with a multimeter?
All the neutrals are tied together. If there are devices on both circuits that complete the circuit (light bulbs, etc.), it's possible to measure continuity as you've described. 

You'll measure from probe 1, along the neutral of circuit A, back to the panel. Then along the neutral of circuit B, across the load (light bulb, etc.) to probe 2 on the hot of circuit B.