OK, let's be clear. Yes, the router will use its MAC address as the connection to the other side which is why a router is fine for this. But, the problem is that routers are normally connected to "the other side" (or man behind curtain in your parlance) using Ethernet to another router (e.g. the Hotel's) or a modem (DSL or Cable or whatever). A router does not normally connect via Wifi to an access point like this.
The specs listed for Airport Express on Amazon do not suggest you can use it this way, which is why I am asking.
So, you are saying you can connect your computer to the AE (somehow) and then it will (a) let you control it to connect to the access point of the hotel using their SSID, and (b) allow your browser to get redirected to their signin page (pay page usually), and then (c) make a wireless network for other devices in the room?
If so, that is great. But, I want to be clear that the AE page at Apple and at Amazon do not suggest that at all. Instead, they focus on plugging the AE into a hotel's Ethernet cable to create a room wireless network. This is not an option since most hotels do not have an Ethernet cable anymore. Instead, it has to connect to the Hotel's wireless (as noted above) and then connect to the devices in the room using wireless meaning two radios and not what they suggest it can do at all.