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Carrier firewall policies generally allow any outbound traffic. Some carriers in specific countries may have more restrictive policies for either regulatory or carrier-specific reasons, such as the United Arab Emirates Telecommunications Regulatory Authority mandating all VoIP services obtain licenses[1], resulting in specific blocks on VoIP traffic such as Skype, WhatsApp, Viber, etc.[2].

[1] https://www.tra.gov.ae/en/faq.aspx (check out the VOIP section)

[2] http://gulfbusiness.com/snapchat-voice-and-video-calling-blo...

Don't see why not -- many popular VoIP protocols run over UDP.

Lots of video games (including mobile) use UDP so I'd be very surprised if mobile networks blocked UDP.

In Finland, the big operators use CGN by default. So if it works, it only works as a one-way street and p2p or hosting your game at home is no-go.

At least one operator allows you to lift the restriction though. With money.