If the sender adds the required headers into his email then it is very likely that google or any other email service provider will not consider the email as spam.
Regarding facebook I partially agree with u. Sometimes the message from non-friends goes into other folder and sometimes I can see it in the regular mail folder.
Adding the proper headers such as DKIM, SPF, etc., are used to make sure a spammer can't send mail pretending to be someone else.
All spam systems still look at the content of the message plus the reputation of the IP/domain when determining if a message should be marked as spam or not.
Don't tell the spammers making millions of dollars about that header trick.
Seriously though, I don't think a couple of headers will cause an email to become not spam. Google's filter is probably Bayesian, and considers the content of the message, the matching between the originating server and the reply-to address, the spam history of the originating server, any links in the message, how many times it sees the exact same message, how many people mark it as spam, etc.
So maybe it will get through to the first few hundred people, and then they'll block it.
Regarding facebook I partially agree with u. Sometimes the message from non-friends goes into other folder and sometimes I can see it in the regular mail folder.