Depends on what is broadcasting from the tower.
Typical cell frequencies are different enough from 2.4/5.8 wifi frequencies that they won't interfere. This is by design. 2.4/5.8 is designed for consumer use so that it doesn't interfere with communications.
What will interfere is 1.2-1.3ghz signals, frequently used by amateur radio operators. So, if you are near a HAM repeater, it may throw off your 2.4 control. I'm not sure if municipalities operate these, or just hobbyists, but it is a possibility all the same.