You should be able to create a task that uses the External ServiceLink "Dummy" adapter to auto-close the task. I use that frequently with authorization tasks to send extra email notifications during our service lifecycles. Never tried it with a plan task though.
I don't think there is a way to create a service that doesn't have a task plan at all. While you can create a service to auto-close after approval, it would still generate a monitor plan and the auto-close task as part of a task plan.
I have an approval only service like this in production that doesn't use ServiceLink. It has one "fake" task with the condition set to FALSE. Be sure to check the 'Start and complete plan automatically?' checkbox on the plan page.
Once the request has gone through it's 2 approvals, the "fake" task is automatically set to Skipped, the monitor task is set to Completed, and the request is set to Closed.
Below is a screenshot of the service's plan so you can see all the setting
This is not currently possible. Even if you don't configure any task plan at all, the system will create a Monitor task which will stay open until someone closes it by clickling Cancel. So, the only "automated" option here is to create a plan with a single, auto-complete task.