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 runs in Google Compute Engine (GCE), we installed it on a GCE vm using the normal installation procedure and runs quite fine.
A better option would be [Heroku](http://www.heroku.com/). They have a Node runtime available, and should give you an experience similar to GAE.