Indeed.
I've got a couple of non-reworked, near mint, all original parts Eddystones and Remingtons. But I've also got a Winchester (4/18 dated) very much like the one Kragluver describes. The barrel date and serial number on the receiver are correct for each other, and the bolt, wood, and all "major" hardware is Winchester. But, there are a smattering of Eddystone parts. Lower swivel, bolt stop, rear sight.
So, totally original? No. I'm sure it left the factory 100% Winchester. The thing is - and I've been collecting US military for 40 years, so I think I've got a pretty good eye - the rifle "looks" right. It's not a mint piece. It shows some honest use and finish wear. The kind of condition that, not that it could ever be proved (and probably isn't), almost looks like a bring back. In fact, in some ways it's the favorite of my 17's, because it looks like it could have been "over there", like somebody actually did use it in the trenches.
Now, for all I know, those Eddystone parts were put on in the 1950's, and the rifle looks the way it looks because somebody kept it in his barn. But I'm not about to write it off as a parts gun just because it's picked up a few stray Eddystone parts along the way.
One reason, BTW, I think Eddystone parts that tend to show up on rifles made by the other manufacturers, more so than the other way around, is simply that Eddystone made the most rifles, and spare parts were produced as a percentage of parts production for finished rifles. Most spares will tend to be Eddystone parts.
As far as the stock Kragluver describes, I used to have (sold it a couple of months ago) an arsenal reworked Winchester that had a stock with typical Eddystone characteristics, along with mostly Eddystone parts. The foretip, though, was marked with a number 7 instead of the typical Eddystone "E". I was never quite sure what that meant, although I suspect it could have been an Eddystone subcontractor or supplier, with the first time the stock was on a rifle being when it was used on a re-work.
Surprisingly interesting rifles, 1917's, once you get to know them. Good to see them finally coming into their own, in terms of collector interest.