I've had skunks "set up camp" under the shed as well, and I know they aren't after my potatoes. Unfortunately, if you have dogs, they just don't mix well at all. De-skunking a large dog just isn't fun, but it does give you a good excuse for giving them a bath.
I remember when my meathead got skunked during his morning walk (the property's fenced), and he got skunked in the wee hours. As my wife and daughter got him back in the house and were just about to get in the car to head to school, he got into his usually goofy mood. Well, the morning went south from there as both my wife and daughter had to come home from school early..............at the request of others.
Getting back to the IP's question, yes dogs and cats can help if not eliminate the problem. But...........nothing's perfect.