Pros/Cons of using Adhesive on Vinyl Plank Flooring?
Floating floors are a thing because the flooring material will expand and contract over time with the environment of the house.  The subfloor is also going to move, and chances are they are not going to move in the same direction or rate.  Gluing down what is made to be a floating floor can cause joints to open up or buckle.  If the floor moves 1/2" over a 20 foot span, something has to give.

Now, for your project, you're talking about a much smaller scale.  I haven't seen the full plans of what you're doing, but it probably doesn't matter much if you use adhesive or not.  As long as the flooring isn't going to slide off the side of the particle board (rolling a chair around is going to make the floor want to slide), I don't see a reason to use adhesive.  Of course if you did use it, I doubt the expansion and contraction over the 5-6 foot area (total guess) that you have is going to drastically affect the joints.