Can compiler always remove try-catch block if it is proved to be non-throwing?

Consider this:

#include <stdexcept>

template <class T>
void F(T &&t) {
    try {
        t(); 
    } catch(...) {}
}

int main() {
    F([]() noexcept {});             // Call 1
    F([]{});                         // Call 2
    F([]{ throw std::exception{}; });// Call 3
}

I found on clang++-6.0 with flags -std=c++17, regardless of the optimization flags I gave, there is always no __gxx_personality and any exception handling code for Call 1.

Can such optimization be relied on when using a different compiler? I only consider C++11 and above.