Loosing power can cause your Internet connection to go If this happens you will not be able to make calls unless you are equipped with a back up UPS, which could power the connection for a limited short .

Using a UPS to power your modem and VoIP ATA should allow an Internet connection to be maintained for a short duration and should suffice for short local outages. For larger outages the loss of Internet may be more problematic, as for instance a cable company depends on amplifiers to power some of their equipment.If those amplifiers loose power then their system will go down in that area, including both TV and Internet.