Does Google App Engine allow adult content?

It is prohibited.

Prohibited Content
The Content displayed and/or processed through your Application or other web site utilizing the Service shall not contain any of the following types of content:

• Content that infringes a third party's rights (e.g., copyright) according to applicable law;
• Pornographic, obscene or excessively profane content;
• Hate-related or violent content;
• Content advocating racial or ethnic intolerance;
• Content intended to advocate or advance computer hacking or cracking;
• Gambling; Other illegal activity, including without limitation illegal export of controlled substances or illegal software;
• Drug paraphernalia;
• Phishing;
• Malicious content;
• Other material, products or services that violate or encourage conduct that would violate any criminal laws, any other applicable laws, or any third-party rights.

Apparently, the Acceptable Use Policy has changed and now adult content is allowed.

Greg D'Alesandre, Senior Product Manager for Google App Engine has even stated it explicitly here:

I was wondering when someone was gonna notice. This was not a mistake. The new policy does not prohibit pornography nor gambling. The policy was written to disallow illegal activities but to be flexible in terms of the sorts of businesses people are trying to build. While you need to talk to your own lawyers about the legality of the business you build, pornography as a whole is no longer disallowed from acceptable use.

I'd like to correct the answer above with new information: It is now not explicitly forbidden. This is new as of the advent of Google Cloud Platform; You can read their Acceptable Use Policy for full details.