No, that promotion excludes gift cards: (I received that promo in my email and went to the website to look at the terms: copied & pasted from the staples website)
*Limited-time offer. Valid online at staples.online®, our mobile site and Staples iPhone app when you pay with Visa Checkout only. Not valid in store. Limit one discount per customer, nontransferable. Discount is automatically applied to qualifying order when you select Visa Checkout and order is placed. Minimum purchase requirement of $100. Tax and shipping not included in calculating the minimum purchase. Not valid on SKUs 513096 or 1149611, ROKU®, Google products, any Bose®, Canon® ink, Epson® EcoTank™ printers, Epson® ink and toner, HP ink and toner, JBL®, Staples Industrial(sm) purchases, Waonline®, custom printing orders placed online, services, promotional products, gift cards, prior purchases or any purchases on other provider websites. Expires 7/23/16 or when promotional redemption limit has been reached.