Also, how are you planning to attach the bumper rail to its supports and the supports to the main frame?
The side supports will do just fine, though I would recommend adding a lip to them retain the bumper rail horizontally, reducing the load on any weld joint or bolt/gusset. For lack of a better picture, here's a screenshot of a Youtube video as an example
http://i.imgur.com/VhdqrmC.png.
If you secure the front/back supports with gussets or brackets, I can tell you from experience that they will bend from a forward or backward impact (the brackets, that is, the tube will be just fine). Even welding, I would think you'd be risking breaking a weld. You can get creative with the geometry of that support piece so that in rotating backward it both compresses some geometry of its own and reacts against the top surface of your main frame. Edit:
for example