It sounds like the standard pine stand that most of have or have had. I would not take that brace out without replacing it with some temporary support. One method would involve making a leg that will stand inside, at the back of the stand. This leg would be used to rest a longer board that will sit horizontal with one end resting on the new leg. Make this horizontal piece long enough to extend a number of feet past the front of the stand. This end that is outside of the tank can not be rested on top of a chair, saw horse, just about anything that will not fall over. Use something like books to slightly build up the height of the outer support(chair ect...) to the point where you feel this board is bearing some of the weight of the tank, but not so much that you are putting uneven pressure under the middle of the tank.
With some of the weight of the tank transferred to this board you can safely remove the center support. The weight that was being supported by this member has been transferred along that horiz. board to both the temporary leg inside the stand as well as the chair. You may also want to somehow support the leg so that it can not tip over as well. I would also make sure that this leg is resting on something solid. The bottom of these stands are thin and can not support much weight on their own. If there is not a cross member under the floor of the stand, you can add something like a 2x4 layed flat on the floor of the stand. This will help spread the load to a greater area and tend to not deform the floor so much.
It's probably a good idea to measure the distance from the top of the stand to the floor so that you can maintain that distance. In the event there is some deflection due to your temp support, you will want to correct that so there remains even pressure on the bottom of the tank.
When the new sump is in place and you are ready to put things back together, you may want to use wood screws to secure the center support since it is nearly impossible to get those staples to work a second time around.
Hope this helps,
"...but the guy at the LFS said I needed it!"