i think what cece is trying to say is that the swiss CAA wont let him count those hours towards 'requirements' or 'qualifications'.
That, the swiss CAA can do.
But besides that, you would be free to log anything you want. You must only be able to prove it when questioned.
** Oh, and to answer you question, one must know the Swiss's regulations to answer that. But if it says you need an "american license", then maybe a simple "license based on a foreign license" conversion would do, no? For that, go to the nearest FAA FSDO.