No because you cannot post links in the listing profile. And why would you want your reputation linked to their business? You won't be able to resolve anything if they should, say, never clean the place, paint the windows black, or start taking an endless stream of tweekers as guests. Your business is YOU as the host, not the property.
Once they have the listing posted, you can write a reference for them and include some of the best comments about the space Or be their first guest and write a glowing review. A savvy guest will be able to navigate to your profile and see the reviews from when you were that location's host.
https://www.airbnb.com/help/article/334/why-isn-t-a-reference-appearing-on-my-profile