Interesting. Yes. It is possible the TV power supply is being interferred with. However, if this is caused by the cell phone in close proximity, I would certainly expect the behavior to exhibit while the cell phone is ringing.
It is unlikely that there is a significant change in cell phone RF output power, regardless of signalling vs. voice channel. It may change some, but not enough to matter. (i.e., the difference in antenna response vs. frequency, etc.. Really, not enough to be concerned with.)
Perhaps the TV is at fault and it has nothing to do with the cell phone? Could be a problem in the TV's power supply, or the power quality of the branch circuit it is using has a problem. (such as: abnormal line harmonics, bad neutral, bad grounding or bonding, etc..)
You "might" be able to deduce this by trying to replicate the TV problem by selectivly turning ON and OFF certain high-drain appliances in the home, especially those with motors. Air Conditioner, Clothes Dryer (on high heat), Refrigerator, Hot Water Heater, and/or Hot Tubs, Pool Pumps, well water pumps, etc... if you happen to have those.
Based on your last reply, I am beginning to think the problem is not with the cell phone proximity. It just sounds like a coincidence. (??)
To answer one other question, cell phones do not normally "collect and periodically retransmit" data back to the cell site. Some do, but they are very specialized devices. Not your run-of-the-mill consumer handsets.
-mpm