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Hello,
It would not be a problem to run your Tomcat server on your existing Droplet. You can take a look at this tutorial here on how to install Tomcat on your Droplet:
https://www.digitalocean.com/community/tutorials/how-to-install-apache-tomcat-8-on-ubuntu-16-04
Regarding the Pipeline itself, it would really depend on what setup you would like to have at the end, for example, if you like Jenkins to build your Java project and then containerize it and deploy it on the same server? If this is the case you could have a similar setup to this one:
https://www.digitalocean.com/community/questions/running-jenkins-in-docker
That way your Jenkins container would have access to the Docker service on your host, and you can spin up containers from inside Jenkins and start them on your Droplet directly.
If you prefer not to run your app in a container, you could take another approach and share a volume between your Jenkins container and your Droplet, then with the copy command that you already have, you could copy the war file from your Jenkins container to the share volume so that the war file would be available on your Droplet where you could have your Tomcat running.
Regards, bobby