There are different generations/eras of "towers". The ones dating from NMT and the cold war have their own little shrapnel-protected bunkers and most likely UPS:s.
The latest ones which hang on every roof in cities might be turned off, but it just means phones scan until they find 2G/3G signals.
The latest ones which hang on every roof in cities might be turned off, but it just means phones scan until they find 2G/3G signals.