No. When you tick the IP -> DNS -> Allow Remote Requests box, the router will listen on port UDP & TCP 53 and answer DNS queries. It has nothing to do with port forwarding or DSTNAT. The packets will arrive on the input chain of the firewall.
If you have no rules that drop those packets coming from the outside (the WAN side) on the input chain, the default action will be to accept the packets. And the router will process those queries. No port-forwarding rules needed.
You can study this flowchart: The ultimate Mikrotik iptables flowchart - RouterOS / Useful user articles - MikroTik community forum
If there are no drop rules, packets from attacker performing DNS amplification attacks will travel through the boxes with numbers 1 -> 2 -> 3 -> 4 -> 5 -> 10 -> 11 -> 12 -> 6 -> 7 -> 8 -> 9, with nothing stopping them. At #9 the DNS process will handle the queries.
Hence this quote from @holvoetn:
Which you answered with:
If your MikroTik router is from the "home" or "AP" lines of product, then they come with a default firewall configuration where there is a rule at the box #7 (a drop rule on the input chain of the filter table) that drops incoming connections from the WAN side (the condition is "not from LAN"). If you keep that firewall configuration, then it's safe to turn on IP -> DNS -> Allow Remote Requests, because the DNS process will only see packets coming from the interfaces in the LAN interface list.
But if you have the "pro" lines of MikroTik products, such as the CCR or CRS devices, or you have a x86 or CHR license. Then the device comes with zero firewall rules in the default configuration. If you turn on IP -> DNS -> Allow Remote Requests without hardening the firewall, the router will happily answer all DNS queries coming from everywhere.