No, it wouldn't have much to do with a sync failure.
CARP heartbeats happen on the interfaces where the VIPs reside, i.e. a CARP VIP on WAN sends its heartbeats on WAN.
XMLRPC sync happens over the sync interface, it only handles configuration.
pfsync only happens over the sync interface, it only synchronizes states (insertions, deletions, etc)
So a problem with CARP on WAN is nearly always a problem with the switch or connectivity on WAN.