Yes, it's possible. Depending on your threat model, it may or may not be a good idea to have a long-term archive of encrypted data be subject to legal process. Matrix has plans to support IETF MLS, which is a necessary precursor to messenger interoperability.

Matrix lets you configure the history retention on a per-server or per-room basis, fwiw: https://github.com/matrix-org/synapse/blob/develop/docs/mess.... From a metadata perspective, we're working on P2P to avoid metadata accumulating on servers. In terms of the OP here (address-book based contact discovery), https://github.com/matrix-org/matrix-doc/blob/hs/hash-identi... is how Matrix optionally implements it while trying to preserve privacy.