This is very system dependent, it is not possible to give a general answer.
Check the reference below to see the effect of surface relaxation for a specific system
Theoretical study of the nonlinear conductance of Di-thiol benzene coupled to Au(1 1 1) surfaces via thiol and thiolate bonds
K. Stokbro, Computational Materials Science Volume 27, Issues 1–2, March 2003, Pages 151–160