I wasn't really considering that level of integration testing. It would certainly be cool to get detailed error reports from the CI tool. I don't see why you couldn't, since the code is published on the public package system, and you would be getting error listings anyway.
I don't think it would be creepy as long as it's not extracting runtime information from actual users. If it's just CI test results, it shouldn't matter.
Live user data would be a huge security risk. Your CI tests could send you passwords, etc., if they happen to pass through your code during an error case.