Do you need to be a musician to properly perform 4.33? That's a good question.
If all you can perform is 4.33 (or, maybe, the theme song to the Lion King, like my daughters!), you hardly count as a musician. You surely demonstrate interests for the practice, but that's not tantamount to being an actual musician (or only in a very limited and obscure kind of way). At best, it makes you capable of performing that one piece.
There's also a difference between performing the piece and experiencing it. I don't think that, in what you describe (getting up, counting time, etc.) you're doing either. I certainly don't think that you're attending to the piece (perceptually attending to the field of sounds); you wouldn't say that you're properly attending to any classical piece of music if you behaved thus.
Now, say you are still performing it.
In the case of a good musician, one can think that she will be able to appreciate her performance as she goes. She'll know, for example, that getting up between intervals would run counter to the experience the specified piece is to elicit and will thus avoid it.
In the case of a poor musician, or a non-musician, the mere act of concentrating on the proper tempo might make it impossible to appreciate the piece while performing it. So in this case, we'd say that the experience of the piece was not adequate.
Though the indications are minimal, there are still indications. A trained musician will have no problem executing those indications while simultaneously appreciating the work thus produced and adjusting her performance to that evaluation. The same is true with any musical piece. Whereas our non-musician will merely be counting time. Someone present at the "performance" of the non-musician will however have the occasion to experience the piece (so long as the non-musician adequately answers to all indications) and so the piece will have been "performed". But that person, sitting at the piano, will not be a musician for all that.
Just as my daughters, though they can play the lion king's theme song, are not musicians for all that.
This is a much more complicated line of argument. It touches on the nature of artworks requiring to be performed in order to be manifest and a possible object of experience. I think you're intuitions are good though: if Cage's piece is problematic as a "musical piece", the issue will likely revolve around the demands placed on the performance and the musicians themselves. As I've indicated, however, I think it wholly possible that the piece be "performed" by non-musicians who can at least recognize the conventions at play in the "performance" (so we're not talking of a neophyte here), but I don't believe that the experience of the non-musician will be identical to that of the musician (if only because the latter can be more attentive to the sonic field that the former, who has to be more concerned with counting the time and so on).