Hi
Most things are possible, however, in this case, probably not practical.
The tool rest has no support at the upper end and the bearings of a drill press are not designed to take radial loads.
If you've never turned 'conventionally' you will have no 'muscle memory' to overcome which will be a benefit.
If you have to go this route, anchor the tool rest to the column and go very easily.
I wouldn't recommend it - perhaps a router lathe type system would suit your requirements
Regards Mick