I am guessing that the housing is wrapped under your tape, and that there isn't actually a hole in the bars. If the housing is continuous, and it probably is, then sure, you should be able to just shove the wire into one end and have it come out the other. I doubt you will need to remove the bar tape.

Sometimes I have to briefly remove the ferrule on the far end, so that I can thread the wire through the tiny hole, and then put the ferrule back on. Just as often though, the wire goes right on through.