GTM Persistence across GTM Sync Group - Listeners are anycasted

I am deploying 4x GTMs in two separate data centers that will all be in the same GTM sync group. The GTM listeners will be part of an anycasted block so queries could come to either data center depending on routing. My question is regarding WIP persistence. If I turn on persistence and a query comes into data center A, to GTM1, that GTM will have a persistence table that will continue to give the same response for a given TTL. Considering anycast, if that same LDNS server makes a second query and anycast takes it to data center B, GTM1, will that GTM have the persistence record that GTM1 in data center A already has?

TLDR: Do GTM sync groups share persistence tables?