You CAN throw a grenade and switch immediately to V.A.T.S. Even if you individually select a grenade just before entering, the interface will simply refuse to let you throw it. It's weird, but you can't throw grenades from inside the V.A.T.S. Use fast travel to hop back and forth between Sanctuary and the areas you are exploring and constantly drop offthe excess materials and weapons you've discovered.

This is hugely useful as Fallout 4's complex crafting system requires you to constantly gather new resources for modding and repair jobs. Dumped your items into a Weapons Workbend? Head over to the nearby Armor one, and you'll see all your items here as well! What's even better, is that all crafting stations are linked.