C++ unordered_map/map [] operator default initialization value

Question

I am wondering if this is a standard that calling [] without assignment will initialize the value of this key-value pair to be 0, if value is of type int?

    // the way I did before, can I skip the if() checking?
    std::unordered_map<std::string, size_t>  word_map;
    for (const auto &w : { "this", "sentence", "is", "not", "a", "sentence",
                           "this", "sentence", "is", "a", "hoax"}) {
        if (!word_map.count(w)) {
            word_map[w] = 0;
        } else {
            ++word_map[w];
        }
    }

Can i do the following instead:

    std::unordered_map<std::string, size_t>  word_map;
    for (const auto &w : { "this", "sentence", "is", "not", "a", "sentence",
                           "this", "sentence", "is", "a", "hoax"}) {
        ++word_map[w];
    }

Thanks.

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UPDATES:

I just checked out this page about en.cppreference.com/w/cpp/language/default_initialization it seems that if we reply on the default initialization int x; the value of x will be indeterminate. So I guess word_map[w] does not necessarily == 0 when first called?