I've never had any issues in doing this with any ROM (stock JB or custom ROMs such as Carbon or PA).
However, I've been giving the new Korean-rip stock KK roms a go and I can't get either one to work correctly with MMS. Paulicat's ROM constantly throws errors saying it can't connect to cell data, so I gave gourab4u's ROM a try. It doesn't throw any error messages at all (and seems to run a lot better/smoother on my phone), but if I try to send an MMS text it never goes through.
Worried that my mucking about with custom ROMs on my phone may have done some weirdness, I LGNPST'd my phone back to stock. The stock JB ROM worked fine with MMS, so I gave both of these new stock KK roms a try again, and the same issues resulted. Just to be absolutely sure it wasn't a radio issue, I flashed this AT&T JB Radio E97020J ZIP. Still no MMS.
Any and all help would be appreciated...the Korean stock KK ROM runs beautifully on my phone otherwise, and I'd hate to have to go back to an AOSP ROM just for MMS.