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: 
Google does support nodejs. So Yes, it is. Start here: <https://developers.google.com/datastore/docs/getstarted/start_nodejs/>
I'm pretty sure that meteor depends upon node.js. I seem to remember in the intro screencast a mention of being "able to deploy anywhere node.js is available".