Unfortunately, for the moment this is not possible.
The approach we had was to considerate the compo like a video layer, because compo can now be precached using "baking into video" feature (only available in smode studio). On which you actually can't play (and loop) until you drag and drop the video inside a timeline or until you create a "local player".
The "local player" is not yet available for compos.
But don't worry we started brainstorming about this ! It's just because adding this feature could cause some modifications on "local player" concepts and we want take the time to correctly harmonize the way playing "video layer" and "compo".