I wasn't able to open the base station, so I relied on the FCC filing photos instead. Based on the photos, the base station's radio uses a CSR BC417 BlueCore4-External device. This a single-chip radio and baseband IC for Bluetooth + EDR of up to 3Mbps. It requires 8 Mbit of external flash, which is supplied by the Spansion chip next to it.
The WHFX30 chip, shown on the base station board in Figure 4, is somewhat of a mystery. Based on what little information I found by Googling it, the chip appears to be a USB controller of some sort.
Figure 4: Base station board
The adapter has an interesting design. As you can see from the FCC filing photo (refer to Figure 5), the antenna is actually housed in the flip-open portion of the case. The design allows the antenna to be oriented in the same plane as the dipole antenna on the conference phone.
Figure 5: Adapter / Dongle opened
A closer inspection of the adapter, shown in Figure 6, reveals that it is also based on CSR Bluetooth silicon, but I couldn't find a reference for the 41814 part number that appears on the chip.