I'm using Game Maker: Studio and already got the UDP broadcasting to work, but only for people using the internet in the same router. But, I want to broadcast via Hamachi too, so there's no need to enter the IP manually.
This is the function I can use: http://docs.yoyogames.com/source/dadiospice/002_reference/networking/network_send_udp.html
And this one I use for local broadcast: http://docs.yoyogames.com/source/dadiospice/002_reference/networking/network_send_broadcast.html
Your gamemaker UDP packets are as good as any other. So if you can send ping requests to an IP, you should be able to send it any UDP packet you want.
When you ping an address through hamachi, you are actually sending UDP packets to it. So if you want to know if UDP communication will work through hamachi, try to ping someone with the console (type "ping [his IP]"). If it works, then any UDP packet with he correct address should travel correctly, including the ones emitted by your gamemaker app.
Be aware, though, that you may have to cope with a greater packet loss ratio than on your local network. Contrarily to TCP, UDP packets may sometimes not reach their destination.
