Yes; if you move each pitch by the right interval, you can move from C major to C♯ major, then D major, etc.
But there is one main caveat to this: assuming you move each pitch by the same interval, this only works in an equal-tempered tuning system (see edit below). Within equal temperament, each half step is precisely 100 cents and each whole step is precisely 200 cents. With those equal and equivalent intervals between each pitch of the initial C-major scale, moving every pitch up 100 cents moves the entire scale up a half step to C♯.
But if you were using another tuning system, you would not have a series of 100 and 200 cents between the pitches of the C-major scale. If you were to move each pitch of, say, a meantone-tempered C-major scale up 100 cents, you would have a mean-tone tempered C♯ major scale that is suddenly in a different meantone system than the original scale.
Doing so would basically destroy the whole point of a meantone-tempered scale. So not only does the action you describe only work in an equal-tempered environment, the very concept is really best fit for an equal-tempered environment.
Edit: I was unclear with the end of my fourth paragraph. The subsequent scale would still be in a meantone temperament, but it would be a different C♯ scale than if you took the C♯ scale within the meantone environment where you took the original C-major scale. As @topo morto succinctly put it, these would be "pitches that weren't in the temperament being originally played, but the notes will still be pitched the same relative to each other." This was my intent.
Furthermore, I didn't realize programs could do work within different tempered systems. As such, this works in all temperaments as long as your program supports it. That's good to know!