No, the upper clip makes it a racerback, so you can't put it on back to front. Actually I could not put any of my sports bras on back to front, as they need to be tight, I would not be able to spin them around.
With this particular bra, you need to do up the clip reaching over your shoulders, like cardoon explains. But it can be possible that you simply can't reach and need to ask for help - I cannot wear their Gym bra for that reason, can't reach the upper clip neither from top nor bottom.