That depends on how the constant is used and in what context. If the value is a literal that would normally be part of an immediate constant in an instruction, then yes, it will consume no extra RAM.
Steen: so it's completely embedded in the compiled code and does not take any SRAM?
What's embedded? That question doesn't make a huge amount of sense. Sorry.
These are likely to take the same amount of code, SRAM, whatever:
int a = 42; ... #define THE_MEANING_OF_LIFE 42 int a = THE_MEANING_OF_LIFE; ... const int TheMeaningOfLife = 42; int a = TheMeaningOfLife;