I think the internet working post power cut is unlikely and consequently your VOIP will go dead as well. Old landline phones will mostly work, the power for your phone comes from the exchange over copper wire and the exchange has massive batteries that will back up the power for at the very minimum a day.. But you still have your mobile and unless you live alone the odds are there is more than one 'mobile device' in the property voice calls should be fine unless the power cut takes out the nearby phone mast and even then unless you live in a very rural area your phone can probably link to more than one mast.