Is it "correct" to specify class-member mutex 'mutable' for the purpose of much-more 'const' member functions?

In many cases, many member-functions could be specified 'const' - they don't modify any data-members of the class ...almost: they do lock/unlock the class mutex. Is it a good practice to specify, in that case, the mutex 'mutable'? ...otherwise, it will impossible to specify get_a(), get_b(), get_c(), get_d() 'const'.

--

A mere example. Lets say that 'example' is a thread-safe class and that m_mutex protects its shared resources that get_a(), get_b(), get_c(), get_d() do not modify:

#include <mutex>

class example
{
public:
    size_t get_a(void) const {
        std::lock_guard lck(m_mutex);
        return m_str.length() + a;
    };

    size_t get_b(void) const {
        std::lock_guard lck(m_mutex);
        return m_str.length() * 2 + a + b;
    };

    size_t get_c(void) const {
        std::lock_guard lck(m_mutex);
        return m_str.length() * 4 + a + b;
    };

    size_t get_d(void) const {
        std::lock_guard lck(m_mutex);
        return m_str.length() * 8 + a;
    };

    size_t modify_something() {
        std::lock_guard lck(m_mutex);
        if (m_str.length() < 1000) {
            m_str.append(".");
            a++;
            b++;
        }
    };

protected:
    mutable std::mutex m_mutex;
    std::string m_str;
    int a = 0, b = 0;
};