It's not a matter if it's a public IP or a private one. But if it's routable from the source to the destination as well as the returning route.
I'm assuming the source (router) sits outside of the FGT and the syslog server's private IP is currently not reachable (no route for that on the router). And another assumption is the router is at the same location with the FGT and the syslog server. They you need to decide if you want to simply route through the FGT since it's secure enough to make a hole at NATed outside-facing interface, or let the router to send syslog to the NAT outside interface then set a VIP to map port 514 to the syslog internal IP.
Sounds like you already decided to do the former, then only thing you need to do at the FGT is to have proper routes, in case those are not directly connected, and a policy from the router side interface to the syslog server side interface to let it come though without NAT. These wouldn't change FW type whatever you have experience with before. Of course the router needs a route toward the FGT for the syslog server IP.