Given how much our lives depend on internet communication, if the global internet were to go down for a week, not only would Bitcoin be down or disconnected, but everything connected to the internet would be affected as well.
Bitcoin would only experience a temporary disruption, and during the internet outage, Bitcoin would not function because the blockchain ledger would be unable to record transfers. However, once the internet is back online, everything would return to normal, including Bitcoin. The network would resume synchronization and new blocks would be added to it, and it would function as usual. So, there's nothing to worry about if it's only temporary.