I had issues when starting conky as a startup application under the unity desktop (Ubuntu 12.04 LTS). The problem is that conky would start in a window that was on top of everything else, rather than on the desktop underneath everything else.
The problem seems to be a timing issue. I solved this by delaying the start of conky by a few seconds. Use the -p option when starting conky to set a pause before actually starting conky. I chose 10 seconds, you can play around with it and find whats works best for you.
Go to the unity dashboard and open Startup Applications, add conky and set a pause using -p. This should start conky automatically whenever unity starts, and allow time for conky to start correctly on the desktop.