Yes, that's exactly what we did. I had an advantage in that I lived within walking distance of the embassy, so I hand-delivered the new passport copy and know it arrived safely. I knew it was attached to my file correctly afterwards because we ordered our GCMS notes a few months later and it showed that we had submitted additional information including an updated passport.
Lunas: I was advised by the US embassy that I would have no issues using the visa issued in my maiden name that is in my old passport with my updated passport, so long as I had my MC available for inspection. Additionally, because I took my husband's last name and did not hyphenate it, my new passport actually shows my maiden name in the format :Charlie D nee (nee = formerly) C. So with both passports (old with maiden name and US visa, new with married name) and my MC, I don't anticipate any issues getting into the US if we decide to go there.
Furthermore, they said if I wanted to change it to my married name I would have to go through the screening and interview process yet again, repay all the fees and there was no guarantee I would be issued a visa again. I said to heck with that!