Almost....not all cellphones are cross compatible across other systems.. The only time that what you describe is a sure thing is if you are either on the primary carrier, or a 2nd tier like Net 10, Boost, etc. that buys their airtime from the primary carrier.. But one thing is for sure: CDMA won't work on a GSM system, and vice versa. Then there is the issue of exclusive bands.. Even if the modulation is the same on another system, the bands used on various systems are MILES apart by several hundred MHz, and the emergency phone, while GSM on a GSM system may simply not be capable of talking on the competitors system. Personally I would never ever rely on an old deactivated phone to save my life. I'll grab the oil' trusty 2mtr HT 1st... :)
The only true flat statement in this thread is that 911 will work on deactivated phones PROVIDING there is cell service, and its compatible with the phone. I still don't buy the "repeater" story unless someone can show a link explaining technically how it works.