Don't use NICAD, use the Lead Acid.

The bigger the battery the longer it will hold up.

The actual time will depend on how much the phones are used during the blackout, what condition the batteries are in, etc

Ask tech support for the maximum draw of the system (or work it out based on the voltage and amperage that the Power supply is rated for (this is written on the power supply)).

I have it but as our power is 240v vs your 120v it may be different.
Then work out how long your batteries will last under that load and you have the minimum.