I know of no reason why you couldn't linear pattern the Part in the Z direction. Select a Plane that's perpendicular to it as your pattern direction and it should work fine.
I just re-read your question. You said "copy a part in an assembly drawing". If this is really a Drawing with drawing views of an Assembly then you'll need to add the second Part in the Assembly itself. However, I suspect you're referring to the Assembly model instead of a Drawing. If that's the case then if the linear pattern won't do what you want (and I know no reason it won't if you want the second one oriented the same as the original), then you might be able to use the "Copy with Mates" feature, or just hold down Ctrl while clicking on the Part (either in the graphics area or tree) and dragging into the graphics area. That will place a second instance of the Part in the Assembly, oriented the same, but it will be unrestrained so you'll need to mate it as required.
I will give it a try, and yes I am working in a .SLDASM file