No, because the software cannot guess for you which handle should be aligned to which other handle. Or to something completely different, like an average angle between any reference points. Chances are, all of these solutions are unlikely to give the intended result, all of them require reworking, so that would not save you an extra step.
However, as soon as you do move a handle, it is clear what you want.
This has been amply discussed on this forum. I’ll dig up the link and add it here.
UPDATE: This is the thread: Smooth points not smooth? - #7 by AlexScholing