I have seen this idea before somewhere, maybe an old woodwork mag from years gone-bye.
I don't like it on several grounds;
The tool-rest is poorly supported, anywhere near the upper end with a dig in and it'll bend. Then heaven help you!
I'm not sure you could 'swing' the tool sufficiently in the 3 dimensions we need to to achieve some of the cuts we make.
A Lathe motor is designed to run constantly, a drill motor is designed to run for short periods, It'll burn out very fast (Electric hand drill motors have a life of around 100 hours usage).