I used shop discover for 15% cashback on a FinishLine purchase and I also used a coupon from FL that I had. Still got the extra cash back.
I think they're pretty stingy with that. I have had cash back not credited to me because I used a coupon code.
If you go to the page for each merchant, you'll often see this
Offer is not valid in combination with any offers found outside ShopDiscover
Of course, if the coupon code is on the ShopDiscover page for that merchant, then you're fine.
Chase Ultimate Rewards seems to be more liberal (although it does depend on the merchant).