For human reviews (EWOQ), there are instructions for google reviewers to scope out suspect 301s by doing comparative whois searches. If the source and the destination whois are the same, apparently that is a good thing in google's eyes as this means the owner simple moved the moved the site. If you 301 to a site with a different whois, apparently that is a very bad thing.
In general, however I suspect similar whois records are not a good thing when it comes to link building (I have no proof of this), but suspect lack of whois diversity to be as bad as lack of c-class, NS, and anchor text diversty when it comes to backlinks.
The thing to know is that google is technically a registrar so they have access to the registrar apis that allow for high volume automated lookups. Whether they can get past private whois, I don't think so, but don't know.
Google (well Matt Cutts) is on record as stating they REALLY don't like fake whois records, which may suggest whois is a strong component in determining search quality, a major tool for google's anti-spam team and perhaps an important factor in google localization (google likes to see locals linking to locals...and that type of info can be parsed/guessed from whois).
Lastly, it is widely suspected that domain age, longevity of ownership, and registration length (google has a patent on this) are factors as well and this is all obtained from whois.
For more dicussion on google's leaked '2011 Google Quality Raters Handbook' and EWOQ see here: