no no no !
If you look at the last comunication from the CAA/DOT on this issue no one except crew and inspectors from the CAA or aircraft operatiors can ride on the jumpseat.
In fact if you read the rules strictly a captain employed by an airline is not alowed to ride on the jumpseat of his employers aircraft if he is off duty.
I an told that BA have an exemption from this rule to let pass holding BA staff ride on the jumpseat.