I don't think so. There are failure modes that GFCI wouldn't catch. For instance, if you managed to grab both the hot and neutral prongs at the same time of the

I don't think so. There are failure modes that GFCI wouldn't catch. For instance, if you managed to grab both the hot and neutral prongs at the same time of the live end of your hypothetical GFCI-protected cord, it may not trip since the current would be passing through you but still returning on the neutral (maybe there'd be enough leakage to ground through your feet/shoes to trip it anyway, but I certainly wouldn't rely on that).