Shopify CLI: Correct, you can develop on any development store and you would then just submit it as a “custom distribution”
https://gyazo.com/325d4be7d5cfcf2bb3c6fef76bc2f27a
As far as your app, that sounds like it would be perfect for a custom app instead of using shopify cli and uploading an app that way. With a custom app you can develop it with the coding language you are familiar with and on your system, and just connect via api keys to your clients store.
When you work with the Shopify CLI, even if the app is free, there are still quite a few things like plans(which still have to be added even if it is free), webhooks to respond to client data deletion requests, and a few other things. OVerall, just easier to build it custom.