Use constexpr hash to calculate enum values and perform user-defined conversion

Is it feasible to use a constexpr hash to calculate enum values and then perform a user-defined conversion?

In the following code, could a constexpr function be used to calculate a hash? Once that is working, would it then be possible to use it in a user-defined conversion?

#include <string>
#include <iostream>
#include <type_traits>

enum class Categories;

#define A 54059 /* a prime */
#define B 76963 /* another prime */
#define C 86969 /* yet another prime */

constexpr std::underlying_type<Categories>::type hash_str(const char* s)
{
    //unsigned h = 31 /* also prime */;
    //while (*s) {
    //  h = (h * A) ^ (s[0] * B);
    //  s++;
    //}
    //return h; // or return h % C;
    return 123;
}

enum class Categories{
    CAT_1 = 1, // CAT_1 = hash_str("CAT_1");
    CAT_2 = 2, // CAT_2 = hash_str("CAT_2");
    CAT_3 = 3, // CAT_3 = hash_str("CAT_3");
    CAT_4 = hash_str("CAT_4")
};

int main()
{
    std::string category_text = "CAT_4";
    int category_string_hash = hash_str(category_text.c_str());
    Categories category = (Categories)hash_str(category_text.c_str());
    //Categories category2 = (Categories)category_text; // no suitable conversion exists
    return 0;
}