Alisson Lima I think I probably made my explanation more complicated than I meant to ... sorry. The issue isn't that we have RFC1918 network overlap at all (otherwise, your answer would make sense). Let me try to explain again:
Suppose at our corporate HQ office we have the network 10.1.0.0/16 (behind the Cisco ASA), and at the data center, we have 10.2.0.0/16 (behind the Check Point 13800 cluster). Currently, across our private link between these locations, we are NAT-excluding 10.2.0.0/16 as traffic heads to 10.1.0.0/16, as we would expect and desire. (Otherwise, all privately-addressed source traffic from the data center would be NAT'ed to whatever we would have defined.)
With our new/planned VPN tunnel, traffic destined for 10.1.0.0/16 (from 10.2.0.0/16) still needs to be NAT-excluded. What I'm not sure of is how that exclusion happens: does it happen because of the VPN domain networks I assign to each "side" of the VPN community (i.e. the 13800 cluster being the hub gateway and the Cisco ASA, as an interoperable device, being the satellite gateway)? Or, does the NAT exclusion happen within the manual rules I have defined under Policy > NAT? Or still yet, do I need both?
I've never built a site-to-site tunnel between Check Point gateways, let alone to a Cisco ASA as a third-party peer. All I need to know is if the manual NAT entries I have in place (without a VPN tunnel) need to remain for NAT exclusion to work over a VPN tunnel, or if I can remove them and instead rely on the NAT exclusion that (I think?) occurs as a result of the VPN domain-defined group of networks within the gateway objects in SMS.
Let me know if that's clearer. Thanks to you all below (Vladimir Yakovlev, Maarten Sjouw, and Chris Atkinson) who also answered.