Yes, it's possible for Fediverse apps like Fedilab to support end-to-end encrypted DMs. We plan to write a FEP where actors expose their public keys in their profile. Each app would manage encryption locally while servers act as relays. The security model is the same as Signal: private keys stay on the device, servers only see encrypted data.
If you have a fediverse account, you can quote this note from your own instance. Search https://toot.fedilab.app/users/apps/statuses/115986491904558099 on your instance and quote it. (Note that quoting is not supported in Mastodon.)
RE: https://toot.fedilab.app/@apps/115986491904558099
There are many interested parties ready to work on e2ee here and we need to figure out how to do this right.