No. Square's product is all about accepting credit cards. From the press release:
"Square will process Starbucks U.S. credit and debit card transactions, which will significantly expand Square’s scale and accelerate the benefits to businesses on the Square platform, especially small businesses, while reducing Starbucks payment processing costs"
"Square will process Starbucks U.S. credit and debit card transactions, which will significantly expand Square’s scale and accelerate the benefits to businesses on the Square platform, especially small businesses, while reducing Starbucks payment processing costs"
https://squareup.com/news/releases/2012/square-starbucks
The Square Register product takes plastic as well as letting people pay via the geo-fencing Pay with Square app.