I've got Piwik on a shared host (WebFaction tier 1) and while I like the software, I discovered its limit at one point last week with http://reasonstumblrwentdown.com. (The site had about 25k uniques and 250k actions total.)

It eventually recovered but I would definitely do some research and further configuration before running the package on a site with high traffic. One friend at a news site told me that they put Piwik on its own VPS before ditching it for performance issues.

Whatever you decide to do, I would run in parallel a backup system from a proven and trusted provider — I scrambled to do so with Google Analytics once Piwik died.