Can CDJs make the instruments in a song you're mixing go out of tune and off key when adjusting the tempo or will the notes being played by?

an instrument always have the right pitch?
Update: spacemissing, Of course the pitch will change of all the instruments in the record equally. I mean when adjusting the tempo on CDJs, do the instruments in the record stay in tune?
Update 2: If you speed up or slow down the record a lot with the tempo adjuster which is like a fader control so you can very gradually adjust the tempo for mixing songs together, does the key of the song change, but the pitch of the instruments is still in tune?
Update 3: Or perhaps there's something on the CDJs that makes the record stay in the same key as the original while you're adjusting the tempo during a mix?
Update 4: Tony B, Thanks for your reply but no, I didn't ask if the instruments in the record will go out of tune with each other. I asked if the instruments can go out of tune in general. Whether when you adjust the tempo, the pitch/tone can be either too high (sharp) or too low (flat) in relation to a standard note... show more Tony B, Thanks for your reply but no, I didn't ask if the instruments in the record will go out of tune with each other. I asked if the instruments can go out of tune in general. Whether when you adjust the tempo, the pitch/tone can be either too high (sharp) or too low (flat) in relation to a standard note reference pitch.
Update 5: spacemissing, Thanks for your update. So do all CDJs allow you to adjust both independently or do some still work like the turntables you're talking about where the tempo control unavoidably changes the pitch at the same time? And if so, and this question can also apply to the turntables and tape decks you... show more spacemissing, Thanks for your update. So do all CDJs allow you to adjust both independently or do some still work like the turntables you're talking about where the tempo control unavoidably changes the pitch at the same time? And if so, and this question can also apply to the turntables and tape decks you refer to, when you adjust the tempo, can the instruments be out of tune, not with each other, but out of tune in the sense that the pitch/tone of the instruments is either too high (sharp) or
Update 6: too low (flat) in relation to a standard note reference pitch, or will the instruments always be on-pitch with a given note?
Update 7: Or I should say, *or will the notes being played by the instruments in the record always be on-pitch with a given note.
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