I do not believe Amazon will see every query in its original state since these queries are sent to productsearch.ubuntu.com and then continue on so your ip address is not reaching Amazon's API. However the other concern is how does Canonical handle these queries since they get them in the original form and have no issued a privacy policy explaining whether any search data is kept.
It is not unreasonable to think that Canonical keeps logs on all of its servers for some period of time and maybe even backups.
They are proxying through productsearch.ubuntu.com with HTTPS encryption (though there's still a a heated bug discussion over whether the search should be included at all). Unfortunately, while no personally identifying information is sent to Amazon, the privacy policy for Ubuntu sharing information about proxied searches is still unclear.
Also, there are concerns that the image thumbnails of results that users download could allow Amazon to correlate queries to IP addresses.
Shuttleworth also wrote a blog post that tries to address the privacy issues with this feature.
I do not believe Amazon will see every query in its original state since these queries are sent to productsearch.ubuntu.com and then continue on so your ip address is not reaching Amazon's API. However the other concern is how does Canonical handle these queries since they get them in the original form and have no issued a privacy policy explaining whether any search data is kept.
It is not unreasonable to think that Canonical keeps logs on all of its servers for some period of time and maybe even backups.
Dash search terms are not sent to Amazon directly. They're sent to Canonical, which then sends them to Amazon. That means Amazon doesn't get your IP.
However, as of the current implementation, thumbnail requests are directly sent to Amazon. So Amazon does get your IP in the end.
More details: https://perot.me/ubuntu-privacy-blunder-over-amazon-ads-continues
That is correct. Dash in Unity leaks information to Amazon and others.
You can read more about the privacy issues and how to fix them in EFF's post Privacy in Ubuntu 12.10: Amazon Ads and Data Leaks.