Moved this to Server Admin. They should be able to help you.

great question, but I think the answer is no right now, you could go submit an idea and it seems like something that would make sense to build into the product.

I had a look at our Tableau server deployment and the custom logo is stored under the following directory which has no delimiter for site.

G:\Tableau\Tableau Server\data\tabsvc\wgserver\images\custom