Is the volume of a protein substrate equal before and after an enzymatic reaction? (pepsin degrading egg white suspension)
The volume of the protein will probably change (although not by much) because it will be denatured as it is degraded and as the pH decreases. As it denatures, the hydrophilic surface area and hydrophobic interior volume will change, leading to a change in the local water liquid structure and density. Denatured, short polypeptides also pack into smaller volumes than native proteins do, and so that would also cause the volume to decrease in most cases. The amount of water in the system will affect the magnitude of the change. I would predict that the volume would decrease slightly, probably on the order of what happens with a few degrees of temperature increase of water (around 0.1%).

So, the short answer is "Yes, the volume will change, but probably not consistently or by enough to be used to reliably measure the extent of the reaction."

This is not my area of expertise, so I don't know what the current standard protocols are for determining reaction rates for pepsin reactions. However, I was able to find a couple of research papers that talk about using ninhydrin to measure reaction extent:

The pH-Dependence of Pepsin-Catalyzed Reactions

Kinetics of Hydrolysis of Egg White Protein by Pepsin

In the second study, they quenched the reaction at a specific time by adding NaOH to bring the pH up, then centrifuged the products before measuring the reaction extent.

If this is not a professional scientific study (meaning it's a school project, or something like that) then you might look at the method used in this report:

The Effect of pH on the Reaction between Pepsin and Egg – White

Basically, they just added pepsin and watched to see how long it took for the solution to become "clear". This won't give you very good accuracy or precision, but it might work for a science project or school report.