Yes, that would be the early "Twisted" (not Twist) barrel. The tube was fabricated by folding a sheet of "Plain Iron" over a mandrel, then welding the long edge

[Linked Image from photos.smugmug.com]

Gervis Francois Magne’ de Marolles, 1789
An Essay On Shooting (An English adaptation of Marolles’ original)
http://books.google.com/books?id=-Q0AAAAAQAAJ&dq

The (Twisted) barrel when forged (is) made to undergo the operation of twisting, which is a process employed by the French workmen on those barrels that are intended to be of a superior quality and price to others; but which as will be seen in the sequel, is very different from that followed by the English workmen in the formation of their twisted barrels. This operation consists in heating the barrel in portions of a few inches at a time, to a high degree of red heat, when one end of it is screwed into a vice, and into the other is introduced a square piece of iron with a handle like an augre and by means of these, the fibres of the heated portion are twisted in a spiral direction that is found to resist the effort of the powder much better than a longitudinal one. To render this operation as complete as possible, it is necessary to observe, that when one the several portions of the barrel have been twisted, the heats that are afterwards given in order to consolidate the fibers of the metal in their spiral direction, by means of the hammer, ought not to be very great. Otherwise the grain of the metal will regain its former state, and the barrel be no better than it was before it underwent to twisting.
From the process it is evident, that to twist a barrel in this manner, throughout its whole length, it must be forged nearly a foot and half longer than it is intended to be when finished, that a portion at each end may be kept cold, so as to give a sufficient purchase to the vise and twisting instrument during the operation: these portions are afterwards to be cut off before the barrel is bored.
The English workmen with whom we have conversed…are all of opinion…that this process of twisting…is really injurious to the barrel, by straining the fibres of metal.

French flintlock with "Twisted" barrels

[Linked Image from photos.smugmug.com]

[Linked Image from photos.smugmug.com]

Thomas Burgeland Johnson, The Shooter’s Guide; Or, Complete Sportsman’s Companion, 5th Edition, p. 157, 1816
http://books.google.com/books?id=5DQCAAAAYAAJ

A common gun-barrel is formed in the following manner. – The workmen begin by heating and hammering out a bar of iron into the form of a flat ruler, thinner at the end intended for the muzzle, and thicker at that for the breech; the length, breadth, and thickness of the whole plate being regulated by the intended length and diameter, and weight of the barrel. This oblong plate of iron is then, by repeated heating and hammering, turned round a cylindrical rod of tempered iron, called a mandril, the diameter of which is considerable less than the intended bore of the barrel. The edges of the plate are made to overlap each other about half an inch, and are welded together by heating the tube in lengths of two or three inches at a time, and hammering it upon an anvil that has a number of semicircular furrows in it, adapted to the various sizes of barrels; and by this means, the whole of the barrel is rendered as perfectly continuous as if it had been bored out of a solid piece.
The barrel, when forged, is either finished in the common way, or made to undergo the operation of twisting; which is a process employed on those barrels which are intended to be of superior quality and price to others. This operation consists in heating the barrel, in portions of a few inches at a time, to a high degree of red heat; when one end of it is screwed into a vice, and into the other is introduced a square piece of iron, with a handle similar to that of an auger; and by means of these, the fibres of the heated portion are twisted in a spiral direction, which has been found to resist the efforts of the powder better than a longitudinal one.
Twisted barrels are deservedly celebrated superior elegance and strength. The iron employed in them is formed of old horse-shoe nails, which are originally made of the softest and toughest iron that can be produced; and which is still further purified by the numerous heatings and hammerings it has under gone in being reduced from a bar into the size and form of nails. Twenty-eight pounds of these stubs are required to make a single barrel of the ordinary size. These barrels are twisted into a spiral form, by means of the anvil and hammer alone, which is not the case with common barrels…

Lots of methodology information here
https://docs.google.com/document/d/1BdbWHfJmr2EyvzcPybid7pwlEliH6m9pr1LxMESM3W0/edit
and
https://docs.google.com/document/d/1oPd3fOeToSHZwCaahXNIyV3sGVqow_Z_ENO8Fnk7kTQ/edit