Possible to use wireless client as the internet gateway?

Consider a setup like this:


Let's first not get into why, but how -

In general in wireless client mode you cannot bridge wlan interface with anything, but I suppose you could still setup nat for say wlan-wan interface without needing to bridge with lan. Has anyone tried something like this - did it work for you? If I configure default gateway on the AP to be 192.168.1.Z which is the wireless client's ipaddress, internet should be routed to the wireless client which then goes through nat to the modem - right?

Now the "why" part

The AP+Router is a ea4500 with poor wifi client throughput (< 36mbps) but good wifi AP throughput (>100mbps). Now of course I can always just connect it directly with the modem, but I would still like to explore if it's technically feasible. In general if I am dealing with ath9k/ath10k I suppose I could just set them up as mesh node to achieve similar result, which sadly mwl8k does not support.

In any case, I would be attempting this setup at some point when I can get convenient physical access to the modem.

I think it is all explained in this guide: https://wiki.openwrt.org/doc/howto/clientmode

Only one thing...

The LAN on both routers can't be must renumber one.

Yes I have done this. I was using routers that can only run stock firmware as bridged range extenders.