Way back when, I had first Trainz2004, then Trainz2009/2010, all purchased on CD. I do not recall if they ran at all without registering them, but I do know that they ran just fine without internet access, unless I was trying to access the Download Station. Likewise, my Trainz22 and Trainz22PE run just fine without an internet connection, but to the best of my recollection, they required that I register them first. The old CD games had serial numbers. Now that I have registered my serial numbers, no-one else can register any copy of Trainz with those serial numbers. While I cannot guarantee this, your CD version of Trains may well turn out to be unusable due to requiring a registration first, a registration that you cannot perform unless the previous owner(s) of the disc never registered. Even if the game works, you will likely be unable to download content for it from the DLS, because that also requires that you have your copy registered if you do it from within the game, and FTP may not be available to you either. I suppose that you could download content with your current game, export it, and import it into the old CD version, but I cannot guarantee that that would work either.
Your current T:ANE should work fine without access to the internet (unless a month-long timer that I don`t know about runs out), but from what I understand, Trains Plus will eventually stop working (and possibly revert to Trainz non-Plus; I`ve had conflicting reports) without the internet.
My recommendation? Back everything up, just in case, and give it a try. I think that you`d have better luck keeping your current install and using it off-line than wiping it for the CD version. You might even be able to have both installed at once, but again, no guarantees. When I installed the second disk of the 2009/2010 twin-pack, it noticed the existing install of the other disc and offered me the choice of installing over or alongside the existing install. Current versions also allow multiple parallel installations, but I haven`t tried T:ANE yet, so I don`t actually know that it will too, but I`d be surprised if it didn`t.