No, the Natural Arch and Bridge Society does not make money from arches.
But some governments do.
The United States Mint released an Arches National Park quarter in 2014 as part of its America the Beautiful Quarters Program, featuring Delicate Arch. You can buy a 100-coin bag of these from the U. S. Mint ($25 face value) but it will set you back $40 with shipping. [UPDATE 2016: Not any more, but you can get a pack of 3 for $9.95 + $4.95 shipping.]
NABS member Daniel Putelat has the following coins in his collection. Quebec released a coin featuring Le Rocher Percé:
He also has in his collection this 2015 Monnaie de Paris (Money of Paris) featuring Pont d’Arc:
Daniel also has in his collection these Monnaie de Paris featuring Etretat:
Paper bank notes have also been produced. Below is Pigeon Rock in Lebanon.
And below is Elephant Trunk Hill in Guilin, China.
And below is an arch in Vietnam.
Don’t spend all your arches in one place!