Did I get the cards?
I've had this happen before, and you do indeed get the cards. You just won't know which cards you earned (unless you remember the number of each card you had before...).
It's happened to me multiple times, with crown chests, free chests, and win chests. I can usually tell that I still got the rewards because of my gold (which I tend to remember) or my gems (in the case of crown/free chests).