No you do not need to boil the malt exrtract, hops, and grains together.
Homebrewing is a step-by-step process. Including the malting of barley a list goes likie this.
1. Harvested barley is malted.
2. The milled malted barley (grist) is mashed for conversion.
3. The mash (soak hot water & grist) is strained/washed/ (sparge) and sent to the kettle.
4. The wort made in the mashing process is boiled with hops.
5. The wort is cooled and sent to a fermenter.
6. Yeast is added and soon it is beer.
7. Package in bottles or whatever.
8. Enjoy
It should be clear now that the grains or malted barley (wheat, etc.) is either used in the mash or in extract brewing steeped in water. But they are not boiled.