Well we have never seen any direct evidence for a privacy protection causing a ranking problem for a domain. But here are some known factors that you might want to mull over:-
Domain History Google has been known to reset domain histories when a domain ownership changes, given too many different ownerships or an expiry and a re-registration (known as a drop) as this is a sign of a new owner grabbing a previously reputable domain for SEO purposes.
Privacy – at Pubcon in 2006 Matt Cutts the head of Google’ web spam was quoted as saying that it can be sign together with serveral other factors that the owner is a “very different type of webmaster”
WHOIS penalty – We have known Google to use WHOIS information to identify and target domain owners who have a network of sites, it stands to reason that if spammy techniques are in use on one they may well be on the other sites the same owner has ownership of.
So all in all it seems to us that Google certainly considers the WHOIS, ownership and the reputation of domains under common ownership, this is most likely to be of significance when a manual penalty is put in place and a Google reviewer has dug around. We don’t think at this time these factors are used in the regular ranking algorithm.