Quick answer: Yes!
Of course, it depends on whether or not your home exchange partner is willing to take care of your pet while they are in your home. (Or if you are willing to take care of theirs!)
We have a cat (who is almost fifteen years old!) and she has participated in all of our home exchanges. We have a picture of her on our HomeExchange.com page and we also include a few sentences about her in our bio and house profile. So if someone wants to do an exchange with us, they know up front that the cat is part of the deal!
We have also exchanged with a family who had a cat, so not only did we swap homes for a few weeks, but we swapped cats, as well. While our cat probably hid under the bed for most of their stay, our home exchange cat was very friendly and slept at the foot of the bed with us at night.
If you are worried about someone else taking care of your pet, leave them specific directions for what you want them to do. How much does the pet get fed, and when? Where is their food kept? Is the pet allowed to go outside or not? How do you want them to handle the litter box? What should they do in case of an emergency, or what is your veterinarian’s contact information?
It’s best to be as clear as possible what your expectations are for pet care; we had talked with one of our exchange partners about taking care of our cats and assumed they would just know what to do with the litter box. Instead of scooping out the litter box, well… they just kept adding kitty litter until there was a mountain of sand in the box. Oops! Our fault for not communicating that clearly.
We have had people interested in exchanging with us, who come to realize that we have a cat, and have then told us that they are allergic and are therefore unable to complete the exchange. No problem. A lot of people are also very clear that in their profiles that they are allergic to cats so they can’t accept a home exchange request from someone who has cats.
The point is, you just have to communicate that you have a pet, and that the pet is staying in the home during the exchange. People in the home exchange community are typically very respectful of each others’ homes and property, so it’s highly likely that they will take good care of your pets, too!