Yes this is usually the case.
I've attended a few births with private OB's now and basically a midwife will care for the mum while she labours and the OB may (or may not) pop their head in from time to time to check on you depending on whether or not they're around.

Then they will just come in when you're pushing the baby out.
This was also the case at one of my own births where I went private as well.