In my opinion no. If that was the then the web would be a huge mess, think about all the big companies who have thousands and thousands of spam links everywhere just because there brand is known. This would also make SEO a case of damaging your competitors rather than outranking them naturally. Google knows that you can't control 100% who links to your site and unless they see that your buying links or consider yourself to be spamming then they won't punish you for it.

That amount of links won't even appear on there radar.

Dave