If I have 10 domains, all on one keyword, and backlink them.. Will they still count as backlinks coming from the same server?
Yes, they would be counted as backlinks but their weight would be minimal. Two links from different IP are better than let's say 8 links from one IP .
Google will consider the backlinks as the same owner "voting" for their own sites and ignore them for SERPs. You also run the risk of getting a penalty for running a link farm since all sites are targeting the same keyword. Hosting multiple sites on the same server is fine as long as you aren't crosslinking them to manipulate SERPs. I wouldn't do it.