No, only with the Tesla tow package.
Just to avoid confusion "trailer mode" is what they call it when your car is towing something.
"tow mode" is the old name for "transport mode", used to prevent the car going into park when winching it onto the back of a towtruck
I think for a bike rack use, trailer mode will be no advantage. My bike rack with 4 bikes I want to attach comes in at about 78kg so I will pass on the tesla version with its 72kg ball weight rating and opt for aftermarket.