No You Can't.
Unless you are planning on using the pump to only irrigate zone 1.
The controller only sends power to the specified zone when that zone is running. If you hook your relay to a zone, it will only crank on when that zone is on. That's why the MV/Pump terminal is needed for a pump, it sends power to this terminal on every zone.
Your obviously spending some money on converting over, spend a tad bit more and replace your controller!
I personally Recommend these controllers
Depending on how many zones you have
Rain Bird ESPM 4M
Weathermatic Smarline SL1600 -2400
Hunter Pro C