Right now each and everything is connected with internet and technology. The future of banking might happen through blockchain technology and bitcoin in mass adoption. By that time what will happen with the banking process if there happens a termination of internet connectivity for few days time.
n case something like that happens, so, yes it may be a collapse on a global scale. But it must happen something really extraordinary in order to get a situation without connection to the Internet and for some days. It may bring lots of demage for some processes, services or systems that need online Internet connection 24/7, but even in case something could happen it would be for some period of time, and after all people would do their best to cope with the consequences. In my opinion nothing bad would happen to Bitcoin in such case - the Internet would be connected again and everything would be ok.