Google is aware that people are building tools on top of their UI. If they were against it, they could pretty easily thwart it (e.g. by randomizing their HTML/CSS, or by serve different versions to different users). The fact that they haven't taken time to do this is, I believe, evidence that they aren't hostile to these efforts.

Also, I've personally been in contact with people on the Gmail team about this kind of stuff. They are, generally, supportive, but they're very clear that they'll make no guarantees about stability.

They want to see what works and becomes popular.

Why would they not like this? You still need to open up gmail.com. This is pretty much like you scraping google search results.

Historically extensions for Gmail have often been problematic. A lot of people install them and then forget about them, and if something changes, they blame Gmail and there's errors that can't be reproduced. Plus there's the whole security issue of giving third party code access to your mails.