I don't see any problem with a shelf that size sagging. But if it is only supported along it's back edge from a 19mm internal batten them there may be a risk of it drooping at the front. This is the method I use for floaters copied from another forum post:
Fitted a couple of floating shelves today, the principal is the same just use a few more fixings:

The shelves were laminated from 12mm oak veneered MDF with a layer of 12mm MR MDF in the ctr, just right for the 12mm bars. The bit of CLS in the background was drilled on the drill press to use as a jig to get the holes square & level. 4No 12mm black mild steel rods(cheaper than studding), diamond core drill for tiles and 31/64th drill gave a better fit than my 12mm lip & spur drill

Studs were placed in the correct position when I built the wall, so just drilled the tile & studs and set the bars with a drop of gripfill. Did manage to hit a drywall screw

Finished shelves, Will post the whole bathroom/ bedroom/dressing room when its all done but if you want a look (big pics not resized yet)
http://photobucket.com/albums/v156/jasonballamy/Clareville%20rd/Jason