Just echoing what's already been said: It will probably be better if you move it over to the drawer-side of the desk. That way it looks like there are two paths of support along the length of the tank, and (imho, more importantly) the support is closer to symmetrical.
If you leave it over the open part of the desk, I'd be worried that the weight over time would cause the desk to sag, leaving the tank un-level, and possibly in a manner that would cause all of the weight to be focused on a couple stress points.
If you aren't in a rush to set it up, it may be worth leveling the desk, and then piling up ~300 lbs worth of rocks, sand, 5 gallon buckets full of water, whatever. (try to keep it all based on a foot print of the same size as the tank)
Then see if there is any noticeable sagging/deflection (don't trust your eyes, use a straightedge and level) immediately, and again after a couple weeks.
anyways, I think it will probably hold. And I wouldn't suggest screwing it into the wall, At best, I think it would do pretty much very little, and at worst, could tear a bunch of little holes in your wall. unless you are in an earthquake area, then it may be worth throwing some straps around the tank/desk that attach to the wall.