Azure Site Recovery doesn't need connectivity from the primary site to perform the failover.
Refer:
https://learn.microsoft.com/en-us/azure/site-recovery/azure-to-azure-common-questions#what-if-theres-an-unexpected-outage-in-the-primary-region
https://learn.microsoft.com/en-us/azure/site-recovery/site-recovery-faq#if-i-m-replicating-between-two-datacenters-what-happens-if-my-primary-datacenter-experiences-an-unexpected-outage-