There are a few types of licks and figures that would be very difficult if not impossible to play in every key. But these are rare. For instance, if Jerry Lee does one of his gliss rakes across the white keys, essentially creating an extremely fast major scale, how could you do that in F#? It's mostly a sound effect, granted, but there would be no way to finger that F# major scale that quickly.
And there are some grace note type things that you can do with one finger sliding off a black key onto a white key, which would take 2 fingers to do going from a white key to a black key, and this would slightly change how the grace note slur thing sounds. So I'd say no, not absolutely every single thing that is done in 1 key could be done in all 12 keys, but most things can be.

In fact, that is how I've been able to tell sometimes when transpose is being used. There's this really fast country instrumental tune I have a recording of in B-flat. And the piano takes am amazing solo, but in one little spot there is a tiny mistake where his finger hits 2 white keys at once; he gets in the crack rather than hitting the key exactly. Dead giveaway that he was playing the solo in A and transposed it up to Bb, because that mistake wouldn't have been possible in Bb due to the layout of the keys.

[This message has been edited by FAEbGBD (edited 11-12-2010).]