I don't see why some failing/timing out network resource was eliminated here. Fwiw, I'm on 10.12.4 as well and see no issues.
Would look at tcpdump or netstat (look for SYN_SENT connections) while sudo is hung. Also suggest hitting ctrl-t a few times while sudo is busy and see what is going on. Can also dtrace sudo and/or whatever dtrace shows sudo is talking to, and you'll eventually find the problem that way for sure (though you might not be able to fix it, but I suspect you will).