No. Original documents sent to a Swedish authority are usually regarded as public documents and the property of the authority. A vehicle is only supposed to have one set of registration documents at any given time. Your original registration documents are to be replaced by Swedish registration documents when the vehicle is registered here.
Please note that if your vehicle's foreign registration certificate consists of several parts, you will have to send us all of those parts before it can be regarded as a complete registration certificate. Read more about registration certificates from abroad.
According to an agreement between the EU- and EEA-countries, the country of origin is to be notified when a vehicle from that country is registered in another EU- or EEA-country. This means that the Swedish Transport Agency will send a signal to the country of origin containing information about the Swedish registration of the vehicle. The country of origin can then, based on this information, de-register the vehicle there. Because of this you do not have to keep any part of your original registration certificate for the de-registration in the country of origin, since this is handled automatically.