Yes and no. In the current version,
you are able to cure yourself of the Carar and deactivate the Quarantine Enforcement Platform.
However, the final part of the story,
which involves building a rocket ship and leaving the planet,
is not implemented in the main game yet. Supposedly this is because the devs don't want to have the game's ending spoiled before the final 1.0 release, since their Trello page (spoiler warning) claims the game is feature complete (which implies the ending is done but might need bug fixes/tweaks/balancing). However, this is just speculation by fans.
Other than that final part, the game is more or less complete now. If you're looking for more information about the aliens that previously inhabited the planet, you'll have to explore in more detail. There are various research facilities and notes that were left behind that gives some indication about why the planet is quarantined and how they aliens died out. However, the aliens are merely an expositionary plot device and they don't play a huge role in the gameplay.