Sure we can prepare processed foods without preservatives, but in this case we must consume these foods in short time, or for processed foods like not perishable foods which are low in moisture content or high in acidity or contain natural self preservatives.
You can prepare processed foods without preservatives. This depends of the type of food. You can prepare a jam, for example, and you can extend the period of consume if you preserve it in a cold storage. Other aspects as acidity of product help to preserve the product. The moisture content is other important factor for achieve it.
I think we have enough natural food preservatives such as salt, sugar, alcohol, vinegar. as well as boiling, freezing and dehydrating are also in use to elongate the storage period.
preservatives added to exten the shelf life of foods and not always used in prpcessed foods. definatelly yes we can keep processed foods with out preservative such as using, blanching, dehydration, freedrying and concetration. so yes we can