It is strongly not recommended, but you can use a K-type thermocouple with a base unit wired for S-type thermocouple. There will be an inaccuracy if there are temperature gradients between the connection region in the base unit and connection to an internal cold junction of measurement devise. The magnitude of this depends on the length of your furnace, the use of cooling water or not, air and gas convection, etc. So, it is important to keep the base unit pedestal at the same temperature as your measurement devise (normally at room temperature).

Never use the opposite combination: S-type thermocouple with a base unit wired for K-type thermocouple. This gives a large error.