mistergadget
RaceTested 11 Second Club
Mr Gadget's setup, yes. The others, no. The stock oil-to-water cooler is a big cast housing that goes between the engine and the filter. The lower radiator hose has a circuit that feeds radiator fluid to the cooler, which is a finned thing inside that housing. A screw-on adapter leaves that housing in place.
You could use an external cooler any time you are running external hoses, and you could disconnect the stock cooler by replacing the lower radiator hose with a standard F150 one without the extra loop for the Lightning oil cooler. But that would leave that housing just sitting there for no reason. Mr. Gadget's is definitely the way to go if you want to replace the stock cooler.
FYI, for anyone who wants to delete the stock oil/water cooler, you have to use a motor mount on the driver's side from an F-150 without the oil cooler.