I currently run a DHCP server linked with a dnsmasq implementation on my OpenWRT router that connects to the WAN. This allows me to maintain a mix of static and dynamic DHCP leases for clients on my LAN, while updating the DNS domain for the LAN with the client FQDNs and IP addresses. But I really want to move this out of my WAN router and house it entirely in my LAN on RouterOS.

While RouterOS v7 supports DHCP with static and dynamic entrees and does support a DNS server, I can't find evidence of these facilities being linked. Specifically, would the RouterOS DHCP server send updates to the DNS server the the client FQDN and IP address when a client lease is handed out? If this is not built n, is there a practical way to implement this?

The ROS DHCP server can run a script on creation and removal of DHCP leases. Inside those scripts, DNS entries can be added or removed.
Find an example here:
viewtopic.php?t=119469
There are also other similar scripts which you can find using the forum search function.