You won't get increased tension, or even increased downward pressure over the bridge saddles. The angle over the bridge can't really be any steeper unless you're going almost right angle and immediately through the body. If you do that, you get a severe bend in the string, but you may also get the string to push down harder onto the saddle. That could impact tone in some subtle way, though I'm not sure. If you maintain the same angle as with a tailpiece and then turn down through the body, then there will be a bunch of pressure at that turning point as well.
Anyone got a cover for the can of worms I just opened? I thought the whole concept was pretty much covered, but I don't remember us discussing pressure on the bridge saddles previously.
-bob