I need to hack my privets (spelt correctly not “privates”) back taking quite a loot off down t the wood so there will be little to no leaf left on them.

Will they survive and look ok with leaf by autumn?

I’ll bet I’m not the only one who had to read that title twice…

I do mine semi-regularly and it’s fine. They’re really hard to kill IME. Whether it’ll leaf by Autumn I don’t know, but it should be fine by next year.

Once established Privet will take almost anything you can throw at them!
If you are going to take them back to wood though, try not to do it in the main heat of the day and give them a good watering after so they can seal their cuts ok.
Ideally take the cuts back a few inches back from where you want your final hedge surface to be to give it a bit of space to spread out and avoid thick cut ends showing through when regrown.
Also if you want them to green up a bit quicker it’s probably nice to give them a bit of a feed at the same time (pelleted chicken manure is a good idea, give each plant a couple of handfuls and water in well).
After a big hack it’ll come back a little lumpy at first but a few very light trims of the longer stems and it’ll pull back into shape pretty shortly.
HTH