Jond is right, Inserting a rod of any material down that will make no difference to the strength of it whatsoever, the insert still wont be attached to the frame with anything stronger than the bond you get, and it wont be enough.
The rod inserted inside a frame tube works fine but its usually pinned in a few places either side of the break, so you have the insert wleded in, the frame crack welded to the insert and itself and the pins welded in, stronger than it was before it broke.
ADH's sugestion is the best your likely to get, but maybe you could just leave the mast in place so it looks right, it wont make it any stronger to remove it.
I have no direct experience of the product you have in mind, but quite a few car companies bond alluminium chassis together Lotus/Aston, the thing they have that you dont is a substantial area of contact to glue.