I usually prefer to have the provision provided to autostart the spare pump.
1. Autostarting the pump minimizes the upset to the process from losing reflux.
2. Loss of reflux pump can result in an overfill scenario for your overhead accumulator. Once you liquid seal the overhead condensers you are looking at an overpressure scenario. Liquid sealing the overhead condensers might not be an issue depending on the normal vapor stream.
Just what precisely happens depends on your system