If you can run commands/get shell access, then most likely you can copy OCP to the server and run it, since it doesn't require anything special to be installed. I know it's possible with Site5, but I'm unsure about GoDaddy.
Whether or not it's worth it really depends on how fast your pages load now. Even if your page isn't getting a lot of traffic, keeping pages cached gives you a significant boost in Google's search result rankings. My guess would be that priming your pages in some way would be totally worth it, both for user experience and SEO.
Would like to know if there are any issues with using this plugin with shared hosting and even if it's necessary for a site with 3000 posts and 50000 views a day.Cheers.