I haven't had any trouble in the 6 1/2 years I've had my dog. I do clip his claws about every 2 weeks. Frequent clipping makes the "quick" recede so the claws can be kept shorter. Has the dog been crate-trained? If so, he's more apt to stay quiet in the tent, thinking it's just another crate.
A few caveats: First, don't put the dog in the tent until bedtime, when he'll want to go to sleep anyway, especially after "hiking" all day. Second, never, never leave the dog alone in the tent. That's a sure recipe for an anxious dog to claw/chew his way out to get to his humans–he will be more anxious in a strange place. Third, get him out first thing in the morning. Do, firmly, keep the dog off the sleeping bags and inflatable pads–not so much to avoid damage as to save these items for human use. I used to have a lot of trouble with my dog when I was still using a Thermarest–he would gradually slide himself onto the pad and I'd wake up to find myself on the tent floor! Since I changed to an insulated air mattress, that hasn't been a problem–too thick for the dog to slide onto. The dog will need some kind of pad underneath for insulation from the ground–I use a 1/8" Gossamer Gear Thinlight, cut down. Any piece of foam pad will do.
Yes, do keep him away from your food preparation. I generally keep my dog on a tie-out when we're in camp.
I would strongly recommend keeping the dog on leash at all times, especially on his first few trips. Also, train the dog to walk behind his owner when on the trail. The leash is both for the dog's protection and as courtesy to others on the trail. Many otherwise friendly dogs will become fearful and therefore over protective and even fear-biting in strange places. And you don't want him to wander off and get lost or chase wildlife or become dinner for a larger predator.