Whatever the corporate governance arrangements, the main point here is that it is Royal Mail that it is being privatised, not the Post Office.
When governments sell shares they have to strike a balance between getting a high price to raise as much money as possible whilst making sure the sale is not undersubscribed. They also like to see small shareholders make a small profit as it helps generate a 'feel good factor'.
But if the whole stock market goes down after the sale price is set it is possible the value of the shares will drop.
If you want a quick profit i think there's a good chance, although after fees and buy/sell price differences it may be small.
As a long term investment, who knows.