'Hand-in' as an object (the thing handed in) or an event (as you use in your example) makes sense and is not at all unnatural but only very colloquially (you can pretty much form a verb put of any noun in English).
The specific sentence sounds like a (very natural) disfluency of planning the sentence ahead with certain parts of speech filled in the rest expected to be filled in. You're thinking 'thesis' and 'hand in' and time, and you imagine 'the X of the thesis' rather than 'X the thesis'. A rearrangement that is does not use 'hand in' as a noun might be:
When do you hand in your thesis?
When is your thesis going to be handed in?
You would probably only ever use 'hand in' in speech as a quick replacement for the more latinate 'submission', or a more accepted term like the noun for the more specific object being handed in. Using it in more formal written language would sound too colloquial (your newspaper or journal editor would throw you out for it.