Your title tags will impact rankings for all search engines. I would slowly make changes to title tags because massive changes can accidentally trigger some spam filters. Instead of making a sidewide change think about testing one subcategory at a time.
When dealing with title tags you need to look at the length of the title tags and the presence of keywords. If your ads have very short descriptions and/or lack any keywords then it could be helpful to add your internal category names.
If your users are already stuffing keywords into long ad titles, you probably wouldn't want to add anything. Ideally your pages should have title tags that are not too long or stuffed with repetitive keywords.