The asm code that is generated for the const method will be the same if the const is there or not. const is a function of the compiler not the runtime, so if there are any performance gains I would think that the compilers optimizer might use the const as a hint for things like inlining or determining side effects for a possible optimization. So in short the optimizer might be able to help out a bit, but if the method is straight forward to begin with then I doubt that the code generated from the optimizer would be any different const or no const.
Here's an easy optimization I use (rather than hit and miss things like const) which take a second but pay off. Organize your class variables so that they fall on cache line boundaries a little better, and put your most accessed variables together. To do it just put your ints, doubles, floats, etc. together at the top of your class variable declarations and your odd sized variables at the bottom like so:
int foo;
int bar;
double baz;
SomeObject obj;
char ch[14];