does engagement at 32 wks increase chances of early labour?

Hi,
I was just curious. I went in for my check-up today. I am nearly 32 weeks along. Bubs is now 3/5 engaged. He was not engaged at my check up 4 weeks ago, but he has been consistently head down for at least the last 6-8 weeks (maybe longer, but before that I was not sure what I was feeling and the midwife did not check).
I thought the baby only engaged closer to your due date like 4 weeks or so before hand. Does this mean that I have an increased chances of an early labour? This is my first baby.

DD was engaged from about 32 weeks as well. My OB told me at the time that it doesn't necessarily mean you'll go early, just means bubs is in the right position. I did end up going early (at 38wks) but I do know of people going on time or over even with bubs being engaged for a few weeks.

Matilda was engaged slightly at that point & at 40 weeks disengaged entirely. I think they go in & out of that position for a while but its great news that bubs is already in the right place :)