C++ check if statement can be evaluated constexpr

Not exactly what you asked (I've developer a custom type trait specific for a get_value() static method... maybe it's possible to generalize it but, at the moment, I don't know how) but I suppose you can use SFINAE and make something as follows

#include <iostream>
#include <type_traits>

template <typename T>
constexpr auto icee_helper (int)
   -> decltype( std::integral_constant<decltype(T::get_data()), T::get_data()>{},
                std::true_type{} );

template <typename>
constexpr auto icee_helper (long)
   -> std::false_type;

template <typename T>
using isConstExprEval = decltype(icee_helper<T>(0));

template <typename base>
struct derived
 {
   template <std::size_t I>
   void do_stuff()
    { std::cout << "constexpr case (" << I << ')' << std::endl; }

   void do_stuff (std::size_t i)
    { std::cout << "not constexpr case (" << i << ')' << std::endl; }

   void execute ()
    {
      if constexpr ( isConstExprEval<base>::value )
         do_stuff<base::get_data()>();
      else
         do_stuff(base::get_data());
    }
 };

struct foo
 { static constexpr std::size_t get_data () { return 1u; } };

struct bar
 { static std::size_t get_data () { return 2u; } };

int main ()
 { 
   derived<foo>{}.execute(); // print "constexpr case (1)"
   derived<bar>{}.execute(); // print "not constexpr case (2)"
 }

Here's another solution, which is more generic (applicable to any expression, without defining a separate template each time).

This solution leverages that (1) lambda expressions can be constexpr as of C++17 (2) the type of a captureless lambda is default constructible as of C++20.

The idea is, the overload that returns true is selected when and only when Lambda{}() can appear within a template argument, which effectively requires the lambda invocation to be a constant expression.

template<class Lambda, int=(Lambda{}(), 0)>
constexpr bool is_constexpr(Lambda) { return true; }
constexpr bool is_constexpr(...) { return false; }

template <typename base>
class derived
{
    // ...

    void execute()
    {
        if constexpr(is_constexpr([]{ base::get_data(); }))
            do_stuff<base::get_data()>();
        else
            do_stuff(base::get_data());
    }
}

template<auto> struct require_constant;
template<class T>
concept has_constexpr_data = requires { typename require_constant<T::get_data()>; };

This is basically what's used by std::ranges::split_view.