Yes, do scan it. I do think cleaned would be better than a dirty image. Because we want clean Images here, a bad image does get denied or is replaced in time if it's been accepted. You could always digitally clean it. After the scan to keep the ink on. If you don't know how there are people here that can for you.
Also, there is not only one plate. That would be foolish if something went wrong with it. When I worked at a printing shop, we have more than one press rolling Printing the same cards and we were not the only one in the country printing the cards.
What is that behind you!?! Oh, It's me! Looking at the cards you have, That I want. :)