In some situations, it might conceivable hyelp, but in cases like the OP mentioned ("1.5kw and 1.0kw heaters starting up periodically overnight") I really can't see how 'time information' would help, can you?I would suggest that a clue of when something occurs, could help considerably to track down a mysterious consumer.
Indeed, if it were happening 'periodically' throughout the night (which one might expect if it were, say, thermostatically controlled), then the 'unexpected usage' would probably be spread all over the night (so could not be tied to any particular time window by a 'smart' meter), wouldn't it?
Kind Regards, John