Hello
Basically, you can 'fit' 5 fingers on a baby's head. If you're 3/5 engaged, the mw can only feel 2 fingers-worth of head above your pubic bone. And yes, you can go into labour without being engaged at all, though I think this is more likely with second babies.
I am now 40+4 and only started engaging 2 weeks ago. I'm 3/5 engaged today, after a sweep yesterday. I asked the mw today whether she could estimate how long it would take now I'm 3/5...but she said it's not possible.
Hang on in there!