Can Shen teleport Fiora around the map?

Solution 1:

This answer is now out of date due to recent rework of Fiora. See here for updated information.

Yes, but only if Fiora has vision on Shen's ultimate location. The latest Rift Myths just answered this question for us: If Fiora uses her ultimate on Twisted Fate while he is channeling his ultimate will she teleport with him?

It turns out it is based on if you have visibility of where he is teleporting. The first test shows that Fiora will not move with TF if she does not have vision on his final location. The second test she does move because she has vision on the final location.

This also lines up with what Micheal Ayers tested with Nunu.

Solution 2:

As of Fiora's champion update in August of 2015, this mechanic no longer works, as her abilities have been reworked and significantly changed. None of Fiora's new abilities will cause her to follow a teleport/shen ult/tf ult, or similar mechanic.