Does Airport Extreme support WPS functionality at all?
Yes it does.. you might not see it because it is called printer.. but the WPS can support any wireless device.
In your airport utility.. click on the Airport icon so you have the summary page open.. you might also need to click on edit.. but mine worked ok without.

There are two methods.. PIN which is a code supplied by one side or the other..
Or it is done by first attempt.. we recommend the later.. you now have one minute while this is active to connect your aircon to the Airport.

Please note that Mitsubishi has chosen to compromise your wireless network by using and encouraging a broken security method (WPS) for their Kumo Cloud Controller.
This is not the case with Apple router.
WPS will only work in apple router when you do the above procedure.. it will not work otherwise and is turned off.
Nor can anybody connect to the aircon without having physical access to your controller or remote.
WPS is a great idea to help people secure their networks.. WPS is stupidly implemented whenever a router has it turned on by default.. It should be off.. whenever I setup routers I always go through the advanced admin and turn off WPS.. it can be easily turned on when required.. or use external button.. when required.. Otherwise leave it off.
Be happy Apple do not open this security hole by default.
It is the host device that is of concern not the client.