Not with any reasonably installed cell tower. If you were up on the pole next to the antennas, sure. The phone causes that sound because it transmits in relatively high powered bursts that get peak detected by parasitics in the audio hardware in the PC. Basically, the PC acts like an AM radio, albeit a horribly inefficient one. The phone needs to transmit with a lot of power so the tower can receive the signal. However, the tower's antenna is way up in the air and the transmit antennas use a 'pancake' beam pattern that's divided up into 3 (or possibly more) sectors. If you're right next to the tower, most of the signal is going over your head.
The bottom line is that the only reason your phone can cause that sort of interference is because of its physical proximity in combination with its transmit power. A cell tower antenna should be too far away to cause the same interference.