Two areas of a desk that I would carefully consider:-
1) local strength (red oval in pic)
This is the area of the desktop that the clamp holds onto. Assuming each monitor is about 4 kgs (10 lbs), four monitors will have a total of 40 lbs weight that has to be transferred from the clamp to the desktop.
2) table stability
This concerns how the desktop transmits the weight to its legs and then to the ground. If the connection (red rectangle) is not strong or the legs themselves are weak, the table collapses.
The Fredrik's desktop is made of particleboard (which is typical of Ikea tables) whose strength for a 40 lbs force worries me a little. I would much prefer a desktop either of metal or of hardwood.
The Fredrik's connection (ie the 8 screws) between the desktop and support frame looks OK to me. However I have not seen the real product (especially the 4 blue connections) and so I cannot say for sure.
IKEA says the Fredrik is designed to hold up to one 19'' monitor. So, holding 4 monitors (especially all concentrated at the edge) might pose a stability issue.
Lastly, I am not sure if you can find a good sturdy new desk good for your purpose for less than US$100.