Should I enable a feature I created on the same site?
Sure, you enable it. By that you keep track of changes you make on either development environment.

For example you edit some settings on your local dev site, then the activated feature will recognise the changes. Then you recreate the feature and commit the updated files to your repo. On live then you pull the file changes, which your activated feature there recognises as well.

Now you revert the feature on your live site and by that sync the settings you made on dev to live. All by having the feature activated on all instances you work with.