It depends somewhat on the complexity of the language.
Nim uses an interpreter but Nimony, which is destined to becomes Nim 3.0, uses your approach. It will be interesting to how hassles and performance play out there and whether they keep the compile-and-run approach or go back to an interpreter.
Well, I've personally have written a const-expression evaluator that actually reuses the rest of the compiler: it compiles the expression in the current environment with some specific adjustments to the codegen settings, launches the temporary executable and gathers its output... frankly, it's more hassle than it's worth compared to writing a separate const-expression interpreter. Plus, of course, it also runs slower since most constant expressions are usually pretty trivial.