Welcome to the Q&A Forum

Yes, example.com/blog/ will typically perform better than blog.example.com and exampleblog.com, and the more decent links that are pointed to the blog and the main site, the bigger the expected impact from combining them. One word of warning - reverse proxies are complex and many teams encounter major developer headaches. Oftentimes it is easier to find a different way to set up content to be published on a subfolder like /blog/. If you want to leave notes on what type of website you are working on (CMS or other software type for both regular site and blog) I am happy to leave notes if it's one I recognize.