I'd use toilet paper rolls and paper towel rolls instead. They're nice, because you can shake the crickets out, right into the cup. I guess newspaper would work. Are you going to crumple it up, to give them little crevices to hide in?
It should work. You could also take strips of card board and fold them. Like this: ^^^^^ I have everyone in the house trained to save the rolls, lol. I have a basket in the bathroom, and they just throw 'em in.
The cardboard will hold it's shape, but with the newspaper I'd be afraid if a bunch of crickets crawled on top they might weigh it down, smooshing their cagemates. I use the egg crates (just go to your local breakfast restaurant or bakery, and they'll have tons), but have started using papertowel tubes which I think I like better. Just my 2 cents.