I completed a draft of the "Guidelines for the use of Stack Exchange Network Logos and Names" this past weekend.
In the latest draft, use of our logo is not permitted in your product. That was based on the guidelines from this post.
In general, you are probably infringing our trademark if you use one of our logos in your product, because it would be likely to cause confusion as to the origin of your product, so I would advise against it.
Having said that, I raised the issue of adding "fair use" clauses for the purpose of labeling our sites inside your product. Right now it is not permitted so please do not use our logos inside your product while this issue is still under discussion.
I will update this post with updates.