Only if your bow is out of tune, form is off, or the inserts are crooked. The blades on fixed heads act as wings an steer any imperfections making them more prominent.
Here is a quick article I wrote on how to tune your rest to make fixed blade heads shoot the same as your field points. http://www.bowhunting.com/blog/2013/01/31/broadhead-tuning-made-easy/
Related to the article above you can get fairly close when your bow is set up. I always pay a lot of attention to how straight my arrow sits on the rest nicked up. Aligning the entire length of the arrow to the string will provide straight arrow flight. There are a few tools you can use to do this yourself including a laser alignment tool. I use a the cheaper manual arrow alignment tool. Of coarse the arrow has to be the correct weight and spine.... I also like to align my broadheads to my vanes. This is what I do and am acurate out to 50 yards with fixed blade muzzys. Good luck!
Yep - the wings thing. That is why early man put vanes or fletchings on their spears when they began to incorporate the use of an Atlatl. It put a lot more force onto the spear shaft causing it to flex upon release and in the air on its way to the target. The vanes at the end balanced it out and gave the shaft a "consistent" flexure to correct itself in flight.
