I've done it with bar ends on a bike that I ride frequently (on the end of the drops). Unless you wrap it tight as hell, do a long bury (3/4 of the wrap, or so), and then shellac over it, it has a tendency to unravel itself. Other than that, yeah, no problem.

All that said, the traditional way is still to wrap from the ends up. Put a turn of double-stick tape on the end of the handlebar before you install the shifter, then run your shift line to wherever you are going to have it exit the bar tape, holding it in place with a few key bits of electrical tape (or double stick, I guess, since you have it out already). When you're going to start the tape, bevel it as you would when ending the wrap near the top, then cut off the pointed tip, leaving a perpendicular flat section about 1/2 the width of the tape. Between capturing that, and the double stick tape, there will be no problems retaining the tape. After you're done wrapping it up, you can twine it for extra security, if you desire.