Your 2000 Ford F250 Powerstroke Turbo Diesel should will require a smog check in order to be registered in California. It should not require a Catalytic Converter, however we highly recommend verifying this with the Emissions Sticker located in the engine compartment. It will indicate if the truck was shipped from the factory with or without a CAT.
If it was not equipped with a CAT from the factory (there is no indication on the emissions label of a CAT) then you don't need to have one installed in order to pass the smog test. We recommend checking with the previous owner as well in terms of whether they performed any exhaust modifications to this truck.