I would argue that they could not, that the system would change them. The question is if you are then a dwarf fighter dreaming you were a ventrue vampire or if you are now a ventrue vampire dreaming you area dwarf fighter.
I'm of two minds, then, about this... First, we probably mean radically different things by "systems". You seem to (and don't let me put words in your mouth here, but I'm not far from the mark I don't think) consider "systems" to include--for example--Ventrue and dwarves and fighters. I, honestly, consider those not much more than labels or categories. System, for me, is almost exclusively "how to translate intention, aptitude, chance, and environment into occurance". So, less "Ventrue are a part of the system" and more "I can put the label Ventrue--with all its connotation and story elements--onto a D&D racial splat" or less "fighter is part of the system" and more "fighter is what we call this arrangement of traits or dots or build".
For instance, we could call Potence something like "Wackydoo"--and it really wouldn't matter so long as the relationship that label had was the same as Potence. So, it seems terminology isn't the deciding factor so much as the relationship that term's essential components have to other components. That just seems to make sense. Maybe I'm offbase there.
And yet, Secondly, there's the idea of "so what?". If I accept that any change to "Ventrue" literalism (the specific, by the book components) would mean that the result is not actually "Ventrue" (whether I invent a racial D20 splat for it or just alter the discipline package) no matter what I choose to call it, is it possible to tell the same story?
Well, possible, sure. I mean, naturally, what if I had a game that never used Presence (by accident, nobody took it and no NPC had it) and I use a variant of WoD rules where Ventrue don't have Presence--then I could, naturally, have the exact SAME story either way. But, obviously, that's absurd, right? The odds of that are pretty low, so much so that its only technically true.
So, we have to give a nod to the idea that there's a sufficient truth independant of a technical truth--where that Ventrue-with-no-Presence-thought-experiment is technically true... its not really all that meaningful because it doesn't alot for a likelihood or a general accuracy. A more sufficient and reasonable truth would be that if I made Ventrue different, then it would be reflected in your average game. I think we can agree with that, right?
However, if the expectations of the story weren't all that dependant on specificity (the story wasn't particularly Ventrue specific at all, or even so far as to say that the dragon having died by a blade or a bow didn't really make a storyline difference sufficient enough to call a "reasonable truth" difference between them), then one could have the same experience with reasonably different components. So, instead of elven rangers killing a dragon, the same general experience was had (same plot points and same revelations and same mysteries and same player-to-player interactions) even if they'd been human fighters. Or so close as to represent no meaningful difference, despite a technical one.
I would go so far to say that from the looks of it--its entirely possible to use a different system (either in my extremely narrow view of what system is or a more general view) and have the same experience (certainly the same sufficiently meaningful experience). I don't think we're disagreeing about that, actually.
So, can one have the same experience across different mechanics? Looks likely. Across different categories of fluff (elves vs. humans in the dragon example)? Harder, but seemingly reasonably possible. Across genre's? Time periods? Metaphysics (Star Trek levels of far future space fiction vs. old school V:tM)?
That's tougher.