Yes, you can install the server on a machine and access it from your machine.
The easiest way to access it from your machine is to run queries is using neo4j desktop. This will install neo4j browser, allow you to create local database, and give you access to other tools to install.
Once you install server on another machine and have it running, you can access it in neo4j desktop by creating a project and in that project create a remote connection to connect to the remote server. You will need to know the IP address and have an username and password.