the term you are looking for is "seed borne diseases". Here an example of diseases transmitted by cereal seeds, (they discuss pesticides, the point I am trying to make is the diseases, not the treatments) https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/seed-borne-diseases
Diseases can be transmitted in different ways through seeds: either the disease in ON the seed, or it is IN the seed. Some treatments can kill some diseases, mainly bacterial diseases which are on the seeds. Several organic treatments are discussed here:
So to reply to your question: it depends. In some cases, like with potatoes, if you introduce a new strain of Phytophtora outside its native range, it can have a huge impact on the livelihood of many people. In other cases, for example if you transport seeds across neighbouring countries which anyway exchange agricultural products and have other biological exchange, it may have no impact. Crossing natural barriers like oceans or mountains increase the risk.
Researching "quarantine organism" together with your crop name might help find some pathogens.