Not sure if I’m misunderstanding your claim. A string does vibrate as the sum of the string’s harmonics. That’s how pinch harmonics work, and they wouldn’t work if that wasn’t the case.

You poke a spot where a given harmonic doesn’t vibrate, and that takes energy away from the other harmonics that do need to vibrate at that spot.

If we’re just talking about visually being able to see them, I suppose that’s a different question. Maybe on an incredibly low pitched string, or with a strobe light playing at a synced frequency? But in terms of what the string is doing, it is vibrating as the sum of its harmonics.