In a situation where different people could claim IP ownership, will USPTO copyright/trademark filings help the filer's claims of ownership?

I work with a business that recently set up a new LLC that was to be for a new website and related products and services. A software developer was engaged, although no documents at all were signed. The software developer set up a website and did some coding. A week later, things broke up and the software developer and the LLC decided not to work together after all. Now the software developer is claiming all of the company's IP, even though the claims are hogwash, except for maybe claims to code that the business doesn't care about. If the business files a trademark application for the product's name with the USPTO, and if the business also submits a screenshot of the site (and whatever other IP it can) in a copyright filing with the USPTO, will that help defend against the developer's claims of ownership? (The business wouldn't file anything about the developer's code, which it doesn't want.) Thanks.