CB is licensed by rule (like FRS), and CB transmitters must be certified by the FCC (also like FRS). If the SDR you're using doesn't have an identifying label on it, you're probably not allowed to transmit on CB frequencies (of course, monitoring them is fine).
So, aside from the technical question of whether your SDR will transmit in that band, you need to make sure it's FCC-certified. I did a quick search in the FCC OET database, which is where records of equipment authorization are found. CB is regulated under Part 95D, and the search page even has a convenient "software defined radios" checkbox. There were no results with those two criteria. Unless I'm running the search wrong (if someone else gets a different result, please say so), that means there are currently no SDRs certified for use on CB channels.
Monitor away, but know that transmitting with uncertified equipment is illegal, and the penalties can be quite severe. If you don't have one already, maybe you should consider getting an amateur license! You'll get a lot more flexibility in where you can transmit and the equipment you use.