You miss a ridiculous number of interesting camp interactions by not frequently long resting in act one. Act two and three, it doesn’t matter as much. But yes, you do get unique cutscenes if you long rest before you get to the Grove. You get unique dialogue options with companions if you long rest after you talk to Nettie and before you leave the grove.

I can’t emphasize enough, how important long rests are to the story and bonding with your companions, especially in the beginning of act one. The game makes it seem like your problem is urgent, but it actually isn’t. It’s counterintuitive, but you miss great content if you rush.