Audie,
If the original barrel and the new one are standard parts from the same factory for the same model and are both within factory specs, then yes, they should be interchangeable. This assumes your slide (the part you pull back to load the gun) and frame (the part you push the magazine into and which has all the levers and buttons attached to it and, most importantly to government bureaucrats, has the serial number stamped into it) have not been shot out of spec. The problem is all these assumptions. Having a knowledgeable 1911 smith do a detail stripping (pull everything apart, including removing the mainspring from its housing and all that jazz) and detail cleaning and inspection with the new part in place is a very, very good idea. The gunsmith can check everything from barrel engagement and timing to disconnector timing and extractor tension. The reasons this is valuable are that some guns in the past have had some parts that weren’t quite up to snuff and have worn or bent or otherwise failed. Putting in a new part that hasn’t worn together with the old ones will occasionally push something over the edge.
Having said all that, this isn’t rocket science. If you want to learn it for yourself, I applaud that because you will be able to monitor your gun’s condition into the future and that provides maximum safety. I second Countryboy’s suggestion that you get a good book on the subject. Even if you never do the work yourself, better understanding the mechanism and what affects it makes you safer. Better knowing the terminology will enable you to have a more informed conversation with a gunsmith about what might need to be done with it? For a beginning, I would get Hallock’s .45 Auto Handbook, by Ken Hallock. Hallock was a U.S.A.F. Marksmanship School armorer. Russ Carniak once told me Hallock had been his teacher in the Air Force. The information is not elaborate but is very practical. There are good drawings of the gun and the clearest part schematic drawing I’ve seen is included as a fold-out. It relies less on specialized tooling than the next book I’ll mention, which is: The Colt .45 Automatic, A Shop Manual, by Jerry Kuhnhausen. This is the most elaborate and detailed 1911 gunsmithing book. It lays out disassembling and inspecting everything in these guns, using the Colt as the exemplar. It includes photos of what many unacceptably worn parts look like. This is a book you will want to add to your shelf if you think you may ever start working seriously on these guns and want ideas for what parts and tools to acquire? It also differs in some methods from Hallock. All the gunsmithing books differ in some methods, and reading more than one to get a sense of possibilities is important for working on them much.
I know Brownells carries the Kuhnhausen book, but try Amazon. Alibris and Google or Froogle to find the current best prices on either one.
Good luck with it.
Nick