Experiencing the symptoms Nidge described at that low of a level would be uncommon
To answer your questions, yes your basal and bolus requirement should increase.
The nature of the "honeymoon period" is that you're getting some of your insulin from your pancreas. Over time, your pancreas would produce less and you'd need more basal/bolus until (in theory) the point when your pancreas no longer produces any insulin at all. That would be the point (or very close to it) when you would no longer be in the honeymoon period.
The idea behind the "honeymoon" nickname is that things are very easy at first (like being newly wed) when your pancreas still produces insulin. When the newness wears off the marriage can become more difficult just like managing your diabetes when you no longer produce any natural insulin.