No, extensive driving will not be required of your Honda Prelude prior to the smog test because your Honda Prelude is equipped with an OBD-I generation emissions control system which does not utilize "emission monitors".
1996 and later model Honda Prelude's are equipped with OBD-II systems which after smog check repairs (in which the battery may have been disconnected or ECM trouble codes cleared or reset) need to be driven for approximately 400 miles in order to "complete" certain emission monitors required to pass the smog inspection.
You should however drive your Honda Prelude for around 50-100 miles to burn off any CAT residue from the manufacturing process and to get the Catalytic Converter to function at an optimum level.
