I have tried to install modern cartridges on older frames (Raleighs and CCMs) and there is often not enough threading in either side of the BB shell to allow the cups to be fully threaded in. Also, the seat and down tubes and chainstays are often left sticking partially into the BB shell, which does not interfere with old loose ball BB cups, but blocks the wider cartridge threads from going all the way in. I used a Dremel to cut back the tubes before getting a shop to chase or lengthen the threads with their taps.
If the Schwinn in question was made after ~1985 then I suspect these things will not be a problem.