Unless they had a contingency plan in place Parler is dead. There's no way a site that big could be moved in 7 days. ESPECIALLY if they used the vendor lock-in features of AWS.
"There is the possibility Parler will be unavailable on the internet for up to a week as we rebuild from scratch. We prepared for events like this by never relying on amazons proprietary infrastructure and building bare metal products"
So he explicitly says they didn't use the vendor lock-in features, but the "rebuild from scratch" comment sort of contradicts that.
They can do it, it is not hard to replace, for instance RDS with equivalent databases, SQS with something else. The hard part is they will have to find a sane ISP or non far-left marxist company to host or come up with capital for physical hardware and set up colocation or a data center.