Basically yes you can save custom blocs, but any changes you wish to keep as a custom bloc would have to be saved with a modified name, so you could end up with more than one or delete the previous version if no longer required.
You can modify any bloc at any time, but the changes are not saved automatically. Logically if you have a custom bloc then want to change it as a variation any saved version will require a new name. I don’t think you can choose the same name as an existing bloc, however you could delete the original and then use the same name.
These new changes would only appear where you have manually added the new bloc and would not affect previous instances in other projects. I think that would potentially be dangerous.