The only problem I think would be the lack of total time. The bracket they're shooting for is where total time is the holy grail. A person over the summer could do that with Cessna and get maybe a hundred hours. Or they could CFI and get maybe 300. At the end of the summer, that's a pretty big difference.
But, in terms of coolness for an internship, and stories to tell, flying what is no doubt a loaded Skycatcher around the country to fly ins is definitely ranked pretty far up there.