Full Error/Issue: 
Trying to merge¬†{!Account.BillingAddress} onto my google doc template and when I generate document, the value does not merge. I do not receive an error message, it just doesn’t work.

You need to separate the billing address out into individual lines, by street, city, and zip code, etc. Once you separate these merge fields out on your template, the values will merge properly and will still look the same once document is generated.