Yes, provided you activate the Visa/MC before you try to use them on the next transaction.
You could buy one card, activate it, then use it to buy another one, etc., until you reach the max limit per rewards account. This would permit you to stack-up the Staples GCs.
i assume if you have multiple staples stores around you, you can go about to each one everyday to not raise any suspicion (seeing as some stores won't allow you to do that); these shouldn't be gone on day 1 right? lol