It COULD, but it would be unnecessary I believe. A Jockey Pump is there to keep the pressure up in the pipe due to leaks and such, but has nothing to do with the actual operation of the Fire Pump during a fire. That's not typically a function you would worry about during a short power outage.
" We are all here on earth to help others; what on earth the others are here for I don't know." -- W. H. Auden
Thanks for the answers, the feeder to the ATS is already installed with sufficient size to feed both. The MCC is far and want to avoid pulling a second cable. I wonder if NFPA 20 allows to use the ATS power supply for this.
If there is not a fire and a power outage your main fire pump is going to start every time the system leaks down a little. Your going to wear out the fire pump system by starting the whole system.