No a General class ham cannot operate legally below 7.175 however remember that when operating lower ssb when your radio digital display reads 7.175 you are actually transmitting 1.5 kc. lower and that is with a very narrow signal. None of your signal can be out of band. A General should not operate any lower than 7.180 to ensure your signal stays within the band.
A normal SSB radio has a 300-3000 Hz audio and filter response at about -6 dB. This means if you are on 7.128 LSB your signal extends 3 kHz lower, down to 7.125 MHz, at about -6 dB.
The FCC rule is we can't have any modulation products out of our authorized frequency limits. 7.128 would not be safe even for good radio on LSB if the limit was 7.125.
I've heard people right on the authorized band edge, with the modulation products extending 3-5 kHZ out-of-band.