Don't have it, but decided to take a look and see what I could glean from the photos. I assume this is how yours looks?
I assume you are referring to the beam spanning between the left and right posts? (that is how it reads to me, but want to be sure we are talking about the same thing).
If the top shelf is mdf or particle board, I expect it would bow over time without the reinforcement. Often, the bottom side is not finished, so maybe you can tell the material there.
I would not try it. One fear I have is that the screw holes in the shelf from the beam are going to present weak points in the shelf and if it deforms these will quickly cause stress concentrations to start tears in particle board.
I'm guessing the columns are chromed metal tubes and a screw is countersunk into the top surface. If this is the case, I'd recommend you get 4 hockey pucks, drill a hole in the center, and use them as spacers to raise the top shelf (don't know how much clearance you need-hockey puck gets you 1"). Replace the top screws with 1" longer screws.
You may have to notch out the pucks to allow clearance for the beam. Alternately, you can cut the ends of he beam and apply model paint on the cut edge
as long as you are not removing one of the screw locations that hold it to the shelf.
Made of vulcanized rubber, the puck is 1 inch thick and 3 inches in diameter (2.5 cm 7.6 cm) and weighs 5.5 to 6 ounces (156 to 170 grams).---from encyclopedia Britannica
Without having more details on construction and dimensions, I don't know if the hockey puck will work for your situation. This is really more of an example of how you might mod it. Hopefully that gives you the idea for a solution that is inexpensive, looks decent, and works for the tolerances you need.
Let me know if you want a more specific solution and I would be happy to work through it with you.
