Yes, Reader/Acrobat are able to detect and repair some types of errors. The type you're talking about are can be simple to fix, but it would be a mistake to intentionally distribute documents that you know are damaged. Even if Reader/Acrobat were able to correct bad XREF tables in all cases, there are many PDF viewers/consumers out there that probably can't.
Could you give me a brief explanation how does pdf reader fix the file based on a corrupted XREF table? By extracting logical structure from the root object?
I don't have the details or how Acrobat/Reader work, but it's not difficult to rebuild an XREF table if you're able to read the file so you can determine where all of the object are. The PDF specification (ISO-32000) has more information: PDF Reference and Adobe Extensions to the PDF Specification | Adobe Developer Connection