I would doubt that barrels were being made in the New World during that period, but salvaged parts would certainly have been recycled into usable firearms.
Much later than the 17th century, but years ago I saw a number of ML guns from Quebec. These were all restocked, some in pine, all converted to percussion, but the metal parts were from French colonial period arms. One barrel was obviously from a 1717 musket. Some of the stocks were in the style of the original, so I would assume that the broken original stock was available as a pattern, or the restocking was done more or less contemporary with the original period of use of the firearm. Other stocks were more 19th century in style.
A mid-17th century inventory from a house in St. Mary's City, MD listed a few guns, including one that was broken. If it was listed in the inventory, it was obviously considered worth retaining and repairing.
There were a lot of curios made up in 19th century England. The gunmakers who did this work were skilled, and as mentionned, 150 years of subsequent aging could make identification difficult.