⭐ Merited by o_e_l_e_o (4)
Even the NSA have admitted they can still track phones which are in airplane mode, so your phone must still be sending and receiving some data.
Of course, its telephony can see what antennas are around in order to send SOS calls, which can be done without SIM. NSA can find out what antennas the phone was interogating and triangulate/approximate the position.
And if NSA wants to get in your devices, the old phone you start now and then to sign transactions is your smallest problem
But I don't deny it you have a point. Maybe a bit paranoid, but not too much.