Buying Monte vista and Barnacle Bay(from the EA app)

So, as you might know, when you try to buy one of these worlds, it redirects to the EA app.
I dont have EA app on my computer, and don't want it either, but I have the EA app on my other computer. If I buy these worlds on my other computer, will I have the store worlds on my computer that does not have the EA app? The store worlds will be on my store account?