Should my luggage with the exported goods be checked in before Customs?

Generally, no. You must have your goods on you, ready to present to Customs on request for export validation. If you are required to present your boarding cards, you can check in, but you must not drop your bags off until after export validation. In some countries, you MUST check in before export validation.  In these cases, you must ask check-in staff to label your luggage and return it to you. 

Once Customs has inspected your purchases and validated your tax-free forms, they will organize for your luggage to be transferred to the airplane.