I'm thinking not, the washer is supposed to have a standpipe high enogh for suds control.
If too much water went down the pipe to the floor drain, you may wind up with suds on the floor.
If you had a 1/2" tube and not a 1-1/2" pipe, it might fly.
They do make 2" couplings with a 1/2" copper compression fitting for a connection to copper.
Love the drawing though.