The question is unclear to me, maybe you can confirm if I understood it correctly: You have written a servlet, and you want to be able to enable or disable the servlet via OSGI configuration. Is that correct?
The easiest way is to set ConfigurationPolicy to REQUIRED. This ensures that as soon as a OSGI configuration is present the servlet is being instantiated. If there is no OSGI configuration present the servlet is not active (not instantiated).
See acs-aem-samples/SampleOsgiR6AnnotationsImpl.java at master · Adobe-Consulting-Services/acs-aem-sampl... for an example how to do with OSGI annotations.
If the component is not visible, you haven't created a configuration for it. If you use the approach I described above (using ConfigurationPolicy) you cannot use the OSGI webconsole to do it, but you need to create an OSGI configuration in the repository. And if that configuration exists (and only then), the component will be started.