No, not at all.
DNS works above the networking layer, separate those out. So you have:
1. Connectivity: IP addresses provided by NAT, direct connection, etc
2. DNS Database: A list of answers to question
It doesn't matter what you use for 1 as long as 2 is accessible. The answers you provide, the zone files, for 2 should be correct according to the client you want to help.
To please public clients your DNS server must be able to answer questions about its public resources. That can be Forward Lookup or Reverse Lookup. It doesn't matter what you've done for 1 to get the request to the DNS server.
The only question about reverse lookup is whether or not you are responsible for the zone. Reverse Lookup Zones are delegated in the same manner as Forward Lookup Zones. You can see the Delegation path using a tool like Dig.
To lookup the full delegation path for example.com:
dig example.com +trace
To lookup the full delegation path for 4.3.2.1.in-addr.arpa (IP address 1.2.3.4):
dig 4.3.2.1.in-addr.arpa ptr +trace
You may find the lookup for the PTR record stops with your ISP. Reverse Lookup Zones are, by default, delegated to the ISP who owns the IP address block. Whether they delegate further, or how they delegate, is up to them.
Chris