The travelator is carrying you forward against air resistance but as long as your feet are on the moving belt your speed will be the same. If you were to jump vertically then for the short time that you are off the floor you will slow down very slightly due to air resistance and land very slightly behind your original position. Such behaviour is probably against saftey rules.
Now try this one:
A lorry is carrying a load of chickens (or budgies or any bird with wings) in wire cages and approaching a weak bridge. If the birds are alarmed an flapping their wings will it reduce the load on the lorry's axles?