Actually, no.
An AM transmission is made up of a carrier, the Upper Sideband, and the Lower Sideband.
A Single Side Band transmission is the Upper or Lower Sideband, with NO carrier. That is why, when you watch a watt meter, there is NO output on SSB unless there is modulation.
If you are on Channel 40, 27.405 MHz, you are broadcasting and receiving on 27.405 MHz whether you are on USB, LSB, or AM. Of course, the Clarifier can make minor changes in the frequency for fine tuning purposes.
I verified this years ago with my Stoner Pro 40 SSB CB radio. Switching modes did not change the frequency.
I can verify it today, using my Yaesu FT-897D all band all mode transceiver. Whatever frequency I set it on, I can scroll through the various modes (AM, FM, USB, LSB, CW, Digital, Packet, CWR, etc.) and the digital frequency readout does not change.
A 40 channel SSB CB radio does not have 120 channels. It has three different modes of operation on 40 channels.
The SSB operation does have the advantage of 12 watts Peak Envelope Power at 100% modulation (the power output will vary according to per cent of modulation, from 0 to 12 watts), which is much better than the 4 watts output of AM mode.