I think not. Records management in general, and contracts management in particular, should be the responsibility of the business units, or staff groups such as Human Resources, that need the contracts and have to comply with them. The law department drafts and negotiates contracts, interprets them and enforces them, but undervalues itself if it keeps track of contract’s key dates and files them.
Energy trading companies, I have learned from consulting projects, typically have a group of professionals who prepare form contracts and sometimes keep control of them. Those groups ought to work closely with the law department for the new contracts or issues that arise, but otherwise, the work falls into the category of quasi-lawyering. email@example.com