Question: Would it be possible to build and deploy `Meteor` applications on Google App Engine or are these incompatible technologies? 

I know, for example, that `Node.js` is not compatible with App Engine and Meteor seems similar to Node in some respects.

Answer: 
Meteor creates Node.js applications. Google App Engine does not have a JavaScript runtime, but it does have (in beta as of December 2013), [*Managed VMs* which can run Node.js](https://stackoverflow.com/questions/12450321/why-is-javascript-node-js-not-on-google-app-engine/24427331#24427331).

[Google *Compute* Engine (not App Engine)](https://stackoverflow.com/questions/22697049/what-is-the-difference-between-google-app-engine-and-google-compute-engine) supports the MEAN stack (Mongo, Express, Angular, Node.js), so you can run Meteor on GCE.

![Google App Engine screenshot](https://i.stack.imgur.com/6WIFg.png)

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*old answer*

Meteor relies on node.js and as such will not run on GAE until GAE supports node.js, if ever.
Google does support nodejs. So Yes, it is. Start here: <https://developers.google.com/datastore/docs/getstarted/start_nodejs/>