Yes, a DID's current PDS (server) is in its DID document, which is public. https://atproto.com/specs/did#did-documents
For example, my account's DID doc is https://plc.directory/did:plc:fdme4gb7mu7zrie7peay7tst , which says that my PDS is https://enoki.us-east.host.bsky.network .