[uncbuck]

If the Constitution is based on the belief in a 'Creator', is it not therefore logical to assume that athiesm and the Conny are incompatible?

[BMCDA]

The Constitution is not based on the belief in a 'Creator', sorry.
Also, the creator mentioned in the DoI doesn't have to be a supernatural entity. The authors of the DoI could have used 'God' or the name of an other deity if they wanted to be unambiguous about the supernatural origin of the 'Creator' but for some reason they didn't.