It may. To confirm what you're seeing try switching to a different brand of synthetic and see what happens.
I used to have a '95 F-150 that I used synthetic oil in. I used Mobil-1 for about 20,000 miles and then I had the same problem you describe, I was using about 1 quart per 1000 miles. Not seeing any signs of a leak, or any noticable smoke from the tail pipe, I switched to Castrol Syntec and immediately the problem disappeared.
Try switching to AMS OIL. Its about twice the price of Mobil-1, but I am convinced it is superior to other synthetic oils. I'm sure if you ask around you'll find other who will say the same. browse their site and even order factory direct here:
www.amsoil.com
