Initially, you will be measuring the pH of liquid in any case (milk or whey). Once drained, you CAN measure the pH of the liquid that comes off the cheese, e.g., while it is in the press, but there will be a difference between the pH of the whey and the pH of the curd -- I don't recall exactly, but it seems like the whey will be .2 or .3 higher pH than the curd. (Don't rely on that - hopefully someone else will have a more exact memory or data!)
Of course, for a cheese that needs to come out of the press at a given pH (e.g., an alpine style), as the time goes by the amount of whey coming out gets to be very little, so it may get challenging to get a reading!