I think tyre, tube and rim tape have to come off. I don't think that you would be able to depress the nipple inward enough to start it on the new spoke. Even, then you couldn't be sure that it wasn't chewing a hole in the rim tape as you tightened. The final deal breaker is the need to make sure that the spoke end doesn't extend inwardly beyond the base of the nipple - you would file or grind it flush as necessary.
Along the way, it would be advisable to check for any other slack spokes and tension them a little, particularly if there is a some rim run-out in the area of the broken spoke. You can't safely tighten spokes with the tyre and tube in place because you need to make sure that you aren't extending the spoke ends such that they can punch holes in the tube.