As you said the new procedures are not only about the cockpit layout but mostly about new areas of responsability and procedures changed in accordance with those areas.
In this regard the 737 classic is the same as the NG.
Due to the fact that many 737 operators use a mixt fleet classic with NG ,it's very probable that the changes will affect also the classic.
Otherwise it would be difficult to operate on the same time a mixt fleet.On our company this is the case,and the new procedures won't be applied to the NG operations untill the changes will be also done in the classic FCOM's.
It would be very confusing to fly a classic today,by the old procedures,then a NG tomorrow following the new ones.
Brgds....
Alex