In [re.grammar] paragraph 2:

basic_regex member functions shall not call any locale dependent C or C++ API, including the formatted string input functions. Instead they shall call the appropriate traits member function to achieve the required effect.

Yet, the required interface for a regular expression traits class ([re.req]) does not appear to have any reliable method for determining whether a character as encoded for the locale associated with the traits instance is the same as a character represented by a UnicodeEscapeSequence, e.g., assuming a sane ru_RU.koi8r locale:

#include <stdio.h>
#include <stdlib.h>
#include <regex>

const char data[] = "\xB3";
const char matchCyrillicCaptialLetterYo[] = R"(\u0401)";

int main(void) 
{
  try {
    std::regex myRegex;
    myRegex.imbue(std::locale("ru_RU.koi8r"));

    myRegex.assign(matchCyrillicCaptialLetterYo, std::regex_constants::ECMAScript);
    printf("(%s)\n", std::regex_replace(std::string(data), myRegex, std::string("E")).c_str());

    myRegex.assign("[[:alpha:]]", std::regex_constants::ECMAScript);
    printf("(%s)\n", std::regex_replace(std::string(data), myRegex, std::string("E")).c_str());
  } catch (std::regex_error& e) {
    abort();
  }
  return 0;
}

The implementation I tried prints:

(Ё)
(E)

Which means that the character class matching worked, but not the matching to the UnicodeEscapeSequence.