Yep. I ran across one that was converted years ago, and was a drop in conversion. it shot well, couldn't tell it wasn't originally a 380 except for the 32 ACP marking on the slide.
I've seen a few others for sale, and having shot one that functioned fine, I assumed (and we know where that gets you) that it would be the case for all of them.
I just nosed around in response to your PM, and while sometimes it apparently is that easy, sometimes it is not.
It appears that SOME were pretty much drop-in, and some required fitting, specifically the 32 mag well accepting the 380 magazine. If you get a 32 with larger (still in spec) magwell and a 380 mag that is on the smaller side (still within spec) it can be a drop in conversion.
Given the walnut grips your 1903 is a later model. What is the serial # range? Coltautos is a good resource for old colts.
http://www.thehighroad.org/archive/index.php/t-236567.html
http://www.coltforum.com/forums/colt-semiauto-pistols/20518-colt-1903-pocket-hammerless.html
http://thefiringline.com/forums/showthread.php?t=68720
380 barrel here if you decide to give it a go.
http://www.ebay.com/itm/Colt-1908-380-barrel-part-Factory-Colt-380-Acp-parts-/331944383876?hash=item4d496d5584:g:nEUAAOSwU-pXtdkA
Original mags are $$$, but if you're patient they pop up from time to time. I got some original colt military/ parkarized mags (1908 was issued to officers in WW2) for $35 each a couple years ago. Aftermarkets are available, but make sure the seller has a good return policy if you get some taht don't work.
http://www.coltforum.com/forums/colt-semiauto-pistols/98486-colt-1908-380-magazines.html
The 32 versions are a pleasure to shoot. I like them better than the 1908 (same gun in 380).
Buy one of each. Problem solved, no fitting required.