Not directly. But the field emanating from your phone will induce a current in the wiring of the plane if it isn't properly shielded to account for that. So even if there is no physical connection there could still be a resulting interruption in communications. All it takes is a crappy or un-intended ground point somewhere along the signal path or at either end.

One way in which I would stress test new electronics designs for resistance to such interference was to stick a mobile phone on top of it and then call that number. Worked like a charm most of the times: instant crash.