Yes, and this is one reason why eczema is correlated with allergies, because it allows allergens to pass through the skin more readily. And it's probably also a reason why babies put everything in their mouths; they're training their immune systems.
It's possible that if you had more cat dander in your mouth when you were a baby that you wouldn't have developed an allergy. Or, more likely, if you had more mouth exposure to other natural microbes that occur outdoors and around animals, then you would have fewer allergies overall. That is well supported by the evidence.