That's the general notion.
Just curious, how does an oil cooler plug on a new engine? This a reman? If so, from where? Of course, unless there was plenty of nasty left in you cooling system when everything was put together.
Anyways, sounds like you will oil coolering it. Intake gaskets are technically reusable, I generally don't. Easy to mis where they got nicked on the way out.lol
3C3Z 6A642 CA Oil cooler kit I use
3C3Z 9439 BH Intake kit I use
Also make sure you are running a Motorcraft oil filter and OE cap.
Depending on your plans and such, there is a kit to make the cooler and filter remote, move them out at the bumper area. Not neccesary, but some prefer it for servicability and all that.