Iron browser itself offers no extra privacy protection nor anonymity when using third party extensions. It just allows the same extension capabilities as built-in to Chromium. This applies to extensions from Chrome webstore, Iron extensions library, or any other site or third-party.
In general, extensions are written by third-party authors. They can do anything the extensions system allows them to do, including copying and sending offsite to other locations any info which you may give permission for the extension to access. Do you know exactly all the permissions your extensions run with? Do you understand the full implications of what those permissions could allow the extension to do? Not every extension will send your private data away, but you won't know if they do or not just by installing and running them.
In general, to keep your privacy or anonymity secure, you cannot install any extensions at all. Or, you need to download/install the extension, read through all the extension source files from its install directory and see exactly what it is doing. Or else, you are just shooting in the dark.