Dualshock 4 wireless addapter + usb host shield 2.0 - is it possible?

for reasons i wont go on about i cant order stuff online, so i am limited to what usb dongles i can get my hands on from local stores.

the only one i can find that would make sense to work with the rest of the hardware is the dualshock 4 wireless adapter. it almost feels silly to think that the sony brand, controller specific bluetooth interface would not work, yet... it doesn't. OR! im doing something wrong.

has anyone connected the DS4 to the host shield using the PS4 adapter, or know where i can find the info? i have been reading for literally days and with all the information that is out there, i cant find anything that definitively says it does or does not work.

any help will be appreciated