The furnace is above the slab and will probably not be harmed. The metal ductwork under the slab does rust out. You may be able to wet vac the water out from the plenum beneath the blower motor, after you take out the filter. Once your gutters are back up and if you have no more problem then you may want to consider having your ducts cleaned to remove mold spoors.
I would not expect a home improvement store salesmen to have better advice than a tradesperson.