That would be a very bad idea. The oil pump supplies oil directly to some of the bearings. Supplying it through the carburetor will get some oil to the right places, but probably not in the right quantities. Plus it will be diluted with gasoline. I also suspect that the carburetor is not designed to handle oil.
Hook up the plumbing correctly, clean out the exhaust, run the engine, and clean the exhaust again. You should be good to go.