Hi Chris,
I assume you mean an outer ring that the the 3" disc sits in to give it the size/footprint of a standard CD.
In theory it should work as long as the disc is stable in its outer ring.
My understanding is the the B2 CD drive is a standard component but is more like that on a car stereo with no tray that pops in and out.
Brennan support can be more definitive.
I would be wary though because if the adaptor & disc gets stuck it could prove an expensive repair.
I once had a parking ticket get stuck in my car CD player so I have bitter experience !
Why not rip on another device and upload as with your other troublesome CDs ?
John