Online, yes, while if you backed up for the same machine, then it will just start activated.
Either use File - Manage license - Export to save the file, and import later, with entering the key it will first try locally, then if not for the same machine, it will prompt to go online and spend one more.
Or as George stated, backup the whole folder if in doubt, or run the tool from a partition that survives reinstalls.
It should be simple, never needed more than one activation per machine in my tests.
Known complications are only with virtual machines, and unplugging(USB)/disabling network cards.