Simple answer is floor hight.
You have 3/4" subfloor, then 1/2" underlayment, then will add 3/4" flooring on top of it?
In most cases, I would want to remove the 1/2" particle board just to get the finished floor hight correct.
I do not lay hardwood, we have a installer for that
But sure, you can lay the hard wood on the particle board, The nails will reach the subfloor and basically it will work.
If the finished floor hight is what I wanted, I would leave the particle board.
Not often can I even imagine that would want to leave the 1/2" particle board and create a trip hazard entering the room.
And would rather be a little lower by removing the nasty particle board, then leave it and have to step up.
Is just garbage, if I can remove it, I would do it now. Can you ? yes.
Why put down a lifetime floor over cheap particle board that will ruin your floor if it ever gets wet?