Oh boy, you are asking one of "those" questions
The rule: a burnisher needs to be harder than the scraper and polished smooth with no pitting.
So, while its possible the shaft of the drill bit could be harder than the steel of your scrapers, the smooth surface issue might require a bit of work.
Given that Crown, Lee Valley, Hock Tools and Glen Drake all have burnisher options in the $20 range, its a tough sell to do it another way.
But, its possible, and if you like to experiment, have at it.
Folks may likely chime in with how they use carbide router bit shanks, screwdrivers, gouges, chisel backs and dried duck beaks.......
One thing to consider, is "back in the good old days" scrapers were made from old saw blades which were not nearly as hard as the steel in todays scrapers. So, a chisel back might just have been fine.
I recently had my break through with scrapers, and its just a wonderful tool!
Jim