I like to think I would, as I watched golf prior to actually picking up the game for myself. However, if I did not play regularly, my interest in the sport at a higher level would be significantly decreased.
My main reasoning with the difference in interest is the appreciation for the difficulty of the game and how high a level the pros actually play at. When you play the game, and you see a pro stick it within 5 feet from the rough 180 yards away, you sit in awe at the amazing feat that just occurred. If you do not play and see the same thing, you will probably shrug it off and same "Hm, nice shot. I wonder if the Yankees are playing...."