Not sure how much difference it will actually make, depends if the fmc allows for this when calculating an econ speed.
If you are flying at a fixed mach no, then your tas should remain the same (all else remaining equal).
Also depends on the a/c. On the 757 the centre tank is slightly forward of the wing tanks (due sweep), so if you have more than 13 tonnes CofG when you burn fuel your C of G moves backwards. Once you have burnt all centre fuel and start on wing fuel then the C of G will move forward.