Can you render a custom block in a view without adding it to the admin blocks page?
The only purpose of a block plugin is to be placed as a block. It's not an entity. The placed block instance can become an entity of its own but also be part of a layout section.
Since the block is your own custom code you don't need any of the workarounds discussed and linked. It would make more sense to refactor the code and expose it as block plugin to be placed on the page and at the same time as area plugin to be placed in a View.
For sharing the custom code between both plugins you can use classic OOP, or the in Drupal very common traits and services. The service has the advantage that it is more flexible and you can not only share code but also data, for example to cache the result if it is expensive to calculate and used in multiple places.