Mxsmanic wrote:
I know the FCC says you're not supposed to use cell phones on an
aircraft

Actually, the FCC only says that for certain wireless phone
services. Not all of them have that prohibition written in
the regs.

(even though recent studies show that such use does not
overload multiple base stations, as the FCC originally feared).

It's less of a problem now that we've moved away from the original
AMPS (analog) cellular phone. However, the study you are probably
thinking about doesn't say what you are proposing. It is talking
about the Aircell guys identifying that THEIR airborne use (which
is not standard cellular) doesn't cause any untoward interference
to the ground based systems on the same frequency.

However, has anyone tried it on small aircraft?

The problem is that it doesn't work. Once we went to much fancier
digital systems and antenna systems designed to really pack in the
density, trying to hit them from over 1000 feet just doesn't work.

Handheld cell phones have never put out more than 850mw when
operating at high power (and they would use much less in
a plane) and the modern digital ones put out even a fraction of that.
It's unlikely that avionics would suffer much.