For clarity a WAN IP address as supplied by the mobile network. My gateway IP address will remain the same?
That's correct, the path from your internal devices to the TP-Link router remains the same, but on fail over the router will pass your traffic to the 4G network instead of DSL, which means that on the Internet your traffic will be seen to originate from a different external IP address.
Unless you're an Andrews and Arnold customer and using their 4G service, as I think they can route your existing IP address over the backup.
To test your hardware and configuration, you can get a Three SIM with a free 200meg data allowance. That will also check coverage at your location, but the 200meg will only cover one or maybe two speed tests.