The order will not be obeyed. As already stated, FDR will be declared insane and is sent to an asylum.
If I can elaborate a little, General Marshall wouldn't even transmit the order. If FDR went directly to LTG DeWitt, DeWitt would have contacted General Marshall immediately.
If FDR told the FBI to carry out the order, very much doubt J. Edgar Hoover would obey or transmit the order. My guess...Hoover would have called Marshall ASAP.
Then Marshall and Hoover would have contacted Vice President Garner. My guess...Garner contacts Speaker of the House and Senate Majority Leader. These three men see FDR and tell him to resign or be impeached immediately. In view of what's happened, Garner immediately acts as President. Marshall and Hoover publicly state they will follow Garner's orders. No 25th Amendment at this time but FDR can't stay.