CARP doesn't care if it's a tagged VLAN or not. You need good layer 2 between CARP member nodes.
And, yes, if you want all the VLANs to be HA you need a CARP VIP and each member node has to have an interface IP.
VLAN 10
192.168.1.1 CARP VIP
192.168.1.2 Master
192.168.1.3 Backup
VLAN 11
192.168.2.1 CARP VIP
192.168.2.2 Master
192.168.2.3 Backup
etc
etc
Naturally, you set DHCP to give the CARP VIP as the default gateway, DNS Server, etc for each segment as applicable.