This so hard. A constant that replaces a magic number like 5 that is ungreppable, or a constant for a precise number like the physical constants - sure. A constant that replaces a number like 404 or 500 that you want to be able to easily grep across heterogenous code bases for? Pass.
I'll take the momentary ambiguity in some cases (usually quickly resolved by line context and file name) over having to manually hunt down 5 different projects' inconsistently named constants to do 5 different greps any day of the week.