Nick, I say go for it.

A "properly" preformed braze joint using RB CuZn-C will have a higher tensile strength then regular mild steel,although it will lack in ductility when compared. That said, if the joints for welding are clean, properly prepared, fluxed, and the heat is controlled to avoid excess burning of filler elements,  oxidizing, lack of fill causing notching of the weld profile, hey it will work. A proper socket joint for a tube member with a BAg filler will be even better.

With a bit of thinking and planning about joint design go a long way, you bet.

Its a bike frame not the space shuttle rocket booster.

Problem is, most so called good welders don't have the skill or knowledge to weld with the oxy fuel torches ( let alone a decent job at cutting ) and so fear what the don't know. That said, and for the sake of safety, just make sure your up to the skills and go for it.

A Peterson publication book on Welding had a picture of a tube chassis all brazed in a Formula 1 car. Advantages being, low heat input,all position and easy of application, with the emphisis on not needing a GTAW or GMAW power source to do track side repairs.

As most posters mentioned,and maybe with alittle to much zeal, the status quo wants GTAW, what they fail to remember is what was built, hotrodded, customized, modified with good old OAW long before anyone could call themselves a TIG Welder let alone afford to buy one.
From a fella that knows, your more a visionary then a dreamer.

That said, is it outside the norm, yes, outside the relm of a do-able frame,not at all. Good luck.
Noel