Absolutely. Strict Darwinian evolution (which itself seems to have evolved somewhat, although I am not qualified to distinguish the changes on behalf of other readers) mandates that the changes within species are random. The existence of God is predicated on the (quite reasonable) assumption that the universe is planned and therefore not random. If the processes in the universe are random as evolution requires, then Christians must become (or at least place more emphasis on the principles of) deists rather than theists.

Unsolved paradoxes do not necessarily demonstrate that creationism is true, i.e. if proposition A is false, proposition B is not thereby proven true. I certainly believe that creationism is true, but, as a reasonable caveat, I cannot demonstrate creationism to be true ipso facto that evolution is false.