No, there is no exception for driving only a short distance on a tolled road in Hungary. As soon as you enter the country on a motorway, cameras will scan your license plate and check it in the database. If you haven’t purchased an e-vignette you are subject to a heavy fine.
Please note - There should be a grace period. However, from experience we know that the grace period often fails to work as it should be, resulting in fines and problems. Please avoid getting into this situation and buy your vignette up front.
You can order your Hungarian e-vignette now comfortably here.
Related articles:
Which roads require a Hungarian e-vignette?
What happens if I drive without a Hungarian vignette?
Do I need a vignette if I only transit through Hungary?