All neighborhood markets I have checked are coded as grocery stores. I bought a sizable WM GC to use for gas and general WM purchases. (Sam's Club has the cheapest and most convenient gas on my commute. I.E. I get the same CB on gas as grocery, but don't use my card for small purchases.)
AFAIK they have the same policies as any other Walmart so I wouldn't expect to be able to buy any debit GC, but feel free to give it a try