The software is copyrighted whether or not a license is accepted. However, the copyright holders provide a public license (the GPL) that waives some of the copyright holder's rights. For example, the copyright holders waive their exclusive right to make copies, on the condition that whoever makes a copy abides by the requirements laid out in the license. This is effectively a contract that is offered to the public.
Nothing except that license gives you the right to do things that are by default reserved by copyright.
Copyright does not reserve the right to run a software, therefore you do not need permission from the copyright holders, and do not have to accept the license. The GPL makes this explicit for the avoidance of doubt.
Warranties are unrelated to copyright and differ substantially between jurisdictions. Some jurisdictions do not assume implied warranties, others make it impossible to disclaim all warranties. However, a warranty disclaimer is not a contract between author and user, but a shield for the author against claims of damages by the user: if the user has been told that the software is not necessarily fit for any purpose, but uses it anyway and something goes wrong, that's on the user. If the user drags the author before a court, the author can point at the disclaimer and say “I told you so”. But again, this is super jurisdiction-dependent.