The ATA186 simply provides two FXS ports to connect dumb POTS devices. You won't be able to do anything more with the ClearOne than you can with a very basic analog hanset plugged in to the ATA.
We have a ClearOne on a VG224 port (so effectively the same thing as an ATA). To use it for multiparty conferencing we set up the conference using a regular handset (eg 7945) in the meeting room and conference in the analog extension of the ClearOne, so it's just one more party in the conference.
I was amazed that a system as expensive and over-engineered as the ClearOne can't connect via IP and SIP. For all the fancy amps and speakers and expensive mics etc etc etc, you're calling over a POTS line, so quality is never going to be any good. Our room-size ClearOne system never gets used, people prefer the significantly better quality they get using a Cisco 7937 with the extra mics.