I have just gotten finished building an Agriculture related site, It doesn't have any backlinks to it or anything. I currently have a video game site with a PR2 on my homepage, if I put a site wide link to my new Agriculture site will google flag me for Black Hat SEO? It should also be mentioned that both sites have a shared dedicated IP address together.
It'll pass a little juice to you and help get you indexed, but I doubt you'll get any SERP help from it. Plus, 1 link isn't going to penalize you. But..the fact that it's on the same IP will make it even less of a value.
It will not hart you but just help you to get index purpose and you wil not get SERP rank by this link becouse the link niche asre different it;s always good to do link exchange with same them realted site
"Backlink is a Backlink", i believe in that The value may increase or decrease depending on the relatedness of the content on the page from where the link is given, but definitely you get some benefit from a backlink
I do also believe in "Backlink is a Backlink" but the relevancy is also a plus score for backlinks. I would saying this link will not hurt you that fast, if you have releavant links come later to sustained overall your link profile, then your site should be fine. If you keep building links from relevant sites again and again, then it would hurt your site ranking.
I think a site-wide link is overkill and will look spammy. You will get better results from a single link or two.