Yes, pretty much. :) However, we humans do not experience it that way. For example, you might pray for a thing to happen which you would normally think very unlikely to happen. Then, suddenly that thing happens. Did God respond to your prayer? "Sure", I would say. God knew the prayer was coming and whether it was in accordance with His will (in this case "yes".) So, the thing happened. From our POV, it appears that God did something He would not have otherwise done BUT FOR our prayer. I just don't think it works like that from God's POV.
God condescends to use our prayers to do stuff. Moses "dissuades" God from burning up the murmuring Israelites. But do we really think God was upset and Moses calmed Him down or talked Him out of it? Not me.