YES!! They are much more maneuverable than if the designer had built a stable aircraft.
They are so twitchy a human being cannot react fast enough to keep them from destroying themselves.
Hence you answered your own question:
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I'm thinking of the ones that need a computer to fly them
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IIRC, IL2 players complained quite a bit about the P51 Mustang FM's being twitchy.
That is sort of how an airplane with a small enough stability margin to be considered neutral in longitudinal flying qualities will behave.