I think this can work, and it's easy to test: I took a brand new deck of cards, kept the original order (for my own convenience), and asked my wife to draw a line (it would be better to get a clamp next time):


Then, it "accidentally" slipped my hands. It's not even that bad: many cards were still in order and I carefully picked them up:


Face-down, I restored the line as much as possible:


Checking the front confirms they're in the original order again.

It kinda defeats the purpose of hiding data in cards though: you could just as well number the cards to make it even more obvious there's something special with them.