The answer depends a lot on your network setup, which we can't see, so you're going to have to dig a little deeper.
At the root of the issue is that the AirPort Base Station can run in one of two modes... router/NAT mode, or bridge.
The way to think of it is that as a bridge, there is unfettered, open access between the wired and wireless networks - they essentially act as one single network with everything on the wired network being able to 'see' everything on the wireless network, and vice versa.
In NAT mode, the base station acts as a gateway/traffic cop, with two distinct networks (typically wired and wireless), along with rules as to what traffic can pass.
Devices on one side (e.g. wired) typically cannot see devices on the wired side, unless you specifically configure access rules.
Typically you would configure as NAT mode when the base station is the first device connected to your ISP - this creates a control point so all the bad, ugly internet traffic cannot get to your internal network.
You'd use a bridge mode when you have some other device acting at the traffic cop and you simply want to add wireless access to your existing network.
Without knowing more about how your network is setup, it's hard to advise more, other than if you're setting up a mesh then the chances are you have some other router in place that's handling the NAT part, so bridge mode seems more likely.
Note, though, that the AirPort won't integrate with any other vendor's mesh system (meaning you cannot use it at part of the extended mesh network). It's fine to run alongside, but it will create a separate wireless network and your devices will have to decide which network (mesh or AirPort) to connect to.
This may all be moot, though - the chances are any modern mesh system will outperform an old AirPort Base Station, both in terms of performance and reliability, so I'm not sure there's a huge 'backup' use case, but it's your network :)