Yes.. thats the general idea. Same on the ends of the cabinet.
But a sheet of plywood in the same places is even stronger
To get the stand to fold up you have to have enough sideways force to fold up the cross brace or plywood. As you are trying to crush the plywood in an edge on direction this takes huge amount of force. (Think rampaging elephants)
Without some cross bracing you totally rely on the corner joints. If they aren't 100%, or work loose over time then the stand becomes wobbly and could even fail.
If you want a demonstration get a cardboard box, open the top and bottom of it and lay it flat. See how it folds flat really easily. |_| -> /_/ Now tape the bottom closed (like screwing plywood to the back of the frame) Now the box is about 100 times stronger and wont fold flat untill the bottom rips or bends. Same idea when building a tank stand.
Cheers
Ian