I don't know about the effect on multipath. Noise should be the same unless a receiver detects and then takes advantage of an SSB subcarrier signal. In that case, I calculate that LSB-only transmit and receive should increase S/N 3.7 dB. However, using the composite response I measured for one of my tuners (both amplitude and phase), I calculate that LSB-only stereo should degrade stereo separation at higher audio frequencies for analog IFs. For a typical wide IF filter, separation at 15 kHz drops from 55 dB for DSB to 29 dB for SSB. For a narrow IF filter, it drops from 39 dB to 18 dB, assuming the receiver uses a separate stereo separation adjustment for narrow. While I don't think these numbers would bother me much and I suspect most people wouldn't notice the separation loss, they might be enough to prevent general adoption of the method. On the other hand, if the gain in multipath performance were enough, a station might be willing to sacrifice some separation in the extreme treble.
What causes the separation loss for SSB is the slope of the composite response, which is due to the IF filters. The normal DSB subcarrier signal compensates for the slope by combining one sideband that is too low in amplitude and the other that is too high. It works kind of like the vestigial sideband system of NTSC TV. But SSB stereo can use only one sideband, and it is always too high (compared to the DSB level the stereo separation trimpot was adjusted for). The SSB system should work fine with receivers that use flat digital IF filters.
You can download the program and data files I used to generate the numbers here:
http://ham-radio.com/k6sti/SEP.ZIP
It is a DOS program. After unzipping, type SEP at the DOS prompt for instructions.
Brian