The battery backup on the ONT, if present, is specifically for phone service, not internet. You will need to purchase a UPS if you want backup power to the T3200 and even then, they have limits on the battery capacity. PoE would not work as none of the Telus devices support it.
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@LisaO I have batt backup for phone emergency calls only. Battery won't last long with 1 hr calls. less than 6 hrs. In a ups the battery size limits the amount of time it will work The 3200 draws 3 amps at 12 volt so a small ups might last 3 to 6 hours. The ont is plugged into 120 so i don't think internet will be available with power out. You could use a INVERTER generator $1000 plus cheap construction one put out a corrupt 60 cycle that electronics don't like ( square wave 60 cycle ). Only plugged in phone will work no handhelds the base is on 120 plug.