Technical knowledge is a bit rusty - been out the business for a couple of years.. but to answer the question, a cell phone
can interfere with avionics.
The wattage output is not so much the problem, but the signal being sent out from the cellphone 'looking' for a receive signal is. This signal will pulse sensitive electronics and create a disturbance ( flux) in any close proximity wiring - this is what leads to the waving needles and screens on cathode displays. It can be distracting, but worse case is that it can lead to a (LCD) display freeze (last known page scenario). Not that common on big aircraft, but I have seen it on a small business turbo-prop where a cellphone was in a bag in the closet behind the crew, right against the wall - the interference was not only on the TX, but was visible on the panel as well.
Bert and Sebas are also right in that a cellphone is designed to use a single 'cell'. It can and will cross-over in different areas, and can be carried on more than one channel on more than one base station - but - when line of sight is now a good few thousand feet up, the signal will be interogated by numerous cells and depending on antenna direction will tie up many channels while searching for the strongest signal. Cross-over is not the issue, as this happens in town and country driving all the time, but is limited in direction. A 'high density' site, as in Sandton City building (for example) may have 27 micro sites around the building - hand-over is taking place all the time depending on availability and signal strength.
Brings to mind the old story where a vehicle tracking company, using cell tracking, clocked a stolen vehicle at 600 kph...! Turn's out the car was already loaded on a freight plane and airborne..!
Not sure how true, as the aircraft height and shielding may have prevented signal, but the story's a good one..
A cellphone has saved my but while flying tho' - complete electrical failure in a C210, at night, and, of course all Maglite batteries dead, the phone was first used for panel lighting (push any button every 30/40 seconds to turn the light back on) and then to phone the tower 1/2 an hour out..
I also used it once many years back to call Eros tower (Whk) after a mike failure in a little C152.
I see that the US stores now sell a cell-phone to headset converter, so calls can be made and received while flying - for small planes maybe, but not for big and fast.. I don't think it's legal here in sunny SA tho' - will check..
Cheers
R