AFAIK, "no".

However, even if you could, you would have the problem of getting a Swiss vendor (utility company etc) to accept a check from a foreign bank. So, Check out Luxembourg or UK banks (HSBC), where you may be able to do a wire transfer inexpensively.

Best of all... per a recent thread here, an American resident in CH can open an account with PostFinance ... and with UBS (rather ironic, isn't it?).