If yes, does the TLS/cert code handle dual stack addresses?
Sure, that's at a totally different layer. TLS certificates are for a hostname, not an IP.
My experience is, that some server/client implementations check reverse mapping and fail if there is more than one address per fqdn:
[axels-macpro:~] axel% host
cp4.lrau.netcp4.lrau.net has address 91.216.35.77
cp4.lrau.net has IPv6 address 2a02:d40:2:2::77
[axels-macpro:~] axel% host 91.216.35.77
77.35.216.91.in-addr.arpa domain name pointer
cp4.lrau.net.
[axels-macpro:~] axel% host 2a02:d40:2:2::77
7.7.0.0.0.0.0.0.0.0.0.0.0.0.0.0.2.0.0.0.2.0.0.0.0.4.d.0.2.0.a.2.ip6.arpa domain name pointer
cp4.lrau.net.
[axels-macpro:~] axel% ping6 cp4
PING6(56=40+8+8 bytes) 2a02:d40:2:10::121 --> 2a02:d40:2:2::77
16 bytes from 2a02:d40:2:2::77, icmp_seq=0 hlim=62 time=18.691 ms