Should particle board treads be removed before finishing the stairs

I would select the product based on the appearance and durability of the finish laminate alone, with little concern for the substrate material, assuming the substrate is some viable material and not pressed paper pulp or something else obviously inferior.

For identical finish laminates, MDF would be preferable to plywood as it is denser and more dimensionally stable.

The answers of the tread then riser SEEM to make sense, but consider this: A properly installed tread will not come off before the lip breaks off. Using just regular Elmer's wood glue, I used to make treads by gluing the edges of 2 2x6 planks together and then planing and cutting them down (after being clamped for 24 hrs). After that, if I took a sledge to it the plank would never break at the glue joint, but somewhere else along the natural grain. So the stair tread flipping off is highly unlikely. What IS likely is that the overhang could be chipped or damaged and the tread may need to be replaced. If you go riser over tread then you will essentially lock the stairs together to where you cannot remove a single tread in the middle somewhere without tearing up a lot of the assembled stairs. Additionally, locking any wood assembly together completely isn't always good for expansion and contraction caused by potential seasonal humidity change. This isn't always a factor in certain natural climates and/or exceptionally well controlled climates, but if it can be, it should be considered.