There would be hormones floating around in the water and both fish would respond to each others' presence, even if they can't see each other.
What I found works great for a stress-free divider is sandwiching a bunch of java moss between two dividers made of black plastic mesh. You can even put the heater and filter between the two dividers.
http://i761.photobucket.com/albums/x...vamosswall.jpg
(the brown water from IAL makes things hard to see but there's a bunch of java moss between the two dividers)
I didn't like using a single divider because the fish can see each others' reflections on the tank wall when they're both close to the divider, whether plants are around the divider or not.