I don't have original barrels to actually measure, but the 1816 through the 1828 Springfields had barrels too thin to rifle, as I recall. I know the M 1840 barrels were thick enough and I think the M 1832 as well, though don't consider that carved in stone.
If the Pedersoli barrel is on the thick side, that works in your favor, if you wish to have the barrel rifled by someone like Bobby Hoyt.
Gus
Sorry to resurrect an old thread, but I just wanted to add that I have an 1838 dated and Springfield stamped conversion with what appears to be a factory rifling job. At some point the gun was cut down to just two bands, but it appears to be the early style Belgian conversion with rifled barrel. I have never shot anything but blanks out of it.