I would think the dent is on the thinnest part of the tube, and would be subject to overheating and cracking from oxygen embrittlement if you do try it.
The only way to make sure that oxygen is not picked up from the inside of the tube is to purge it with inert gas. You could do that if you find the holes in the frame and run argon or C-o2 throughout that tube. You can find holes in the bottom bracket, seat stay and headtube, as well as breather holes in the chain and brakestays. You could also use balloon helium, but you have to really run a lot of volume and it is pretty expensive. The helium can be gotten easy though.
The flux on the outside is formulated to etch the base metal and keep the oxygen from contaminating the area, so that is ok.
Practice on something first, and see how it goes. I would recommend EasyFlow 56, and the white flux.