Is this really the case with string theory? I know that there are conjectures in particle theory that would require enormous particle accelerators, but have never heard that about string theoretic conjectures.
Regarding the relation between proof and experiment, the computer scientist and mathematician Donald Knuth is supposed to have written this of a theoretical result of his: "Warning to the reader--I have only proved the foregoing to be true, not tested it." -- Curtiss, with volume I of Knuth sitting unopened on his shelf like a reproach