Yes! Most digital repositories are compliant with technical standards that enable cross-archive searching (Open Archives Initiative’s Protocol for Metadata Harvesting OAI-PMH).
A publication or dataset placed in a repository is far easier to find than through an individual's website. Several search engines such as Google or Google Scholar favour OAI-repository material, and display these results more prominently. Moreover, repositories are working to preserve materials in the long-term. The benefit is that if a researcher moves on, or their personal website changes, their publications and data are in a repository - and the links - will remain stable, readable and accessible.

Publisher's policies relating to self-archiving can be found at the SHERPA/RoMEO website.

There are several resources to find repositories: