Can I use 3.8 beta to publish my app to apple store?

Yes, you can if you're comfortable with the runtime stability. Following is an FAQ on that from http://labs.adobe.com/technologies/flashruntimes/air/

Q - Can I release my app using a beta version of the AIR runtime?

A - Adobe does not recommend releasing apps based on prerelease versions of Adobe AIR, however, we will no longer watermark or expire prerelease versions of AIR. Developers that choose to release their apps using beta versions of the captive runtime do so at their own risk, and should test the apps accordingly

-Pahup