A. Yes, but that would not be a tax-smart move. Currently, the FICA tax rate is 7.65% on the first $106,800 of your wages; 1.45% on wages above that figure. But the normal 7.65% rate is reduced by 2% for 2011 only.
If your company pays the FICA tax for you, the payment is treated as additional taxable compensation paid to you. So you would wind up paying FICA tax and income tax on the amount of FICA tax the company paid for you. Not good!