I've seen a couple of elk shot with a 30-30. Never saw one lost with it, they all ended up in the skinning shed. Would it be my first choice? Nope. Will it work? Yep. If I was going to use it I'd keep my shots under 100 yards and I'd hold off shooting until the animal was completely broadside and I'd avoid the front shoulder and shoot for the ribs a little behind the shoulder. I'd also want a good bullet and I'd want it to be 170 grs.
The question is, will a youngster on his first elk hunt be able to control himself like that? A wounded elk can go a long, long ways.