Yes,the k20a harness will work.Basically,any k harness (k20a,k20a2,k24a1 etc..) between '02-'04 can be interchanged,but on the 5 speed transmissions,there is no reverse lock solenoid,only a mechanical reverse lock cam.If you use a harness from a 5 speed,there is no plug for the reverse lockout solenoid.
The harness from an auto will work as well,but will have two extra ecu plugs.