Alfred,
This is a good question. I know several teardroppers that only used the side screws and their installations have been perfectly water-tight. So, I'd have to say that installing screws on the top and bottom is not necessary.
I used Grant's windows also. When I installed the first window on my teardrop, initially I just used screws on the sides. These were sufficient to squeeze out the butyl tape on all four sides. Later for aesthetic reasons, I came back and added the screws along the top and bottom.
You need to be careful on the top and bottom flanges because they are not as stout as the side flanges. Too much screw torque can bend the flanges. If you decide to add screws to the top and bottom, it is much easier to drill the flanges on the bench before the window is in place. That is what I did on the second window.
Take care,
Tom