Well.. to be frank, this is workable but quite some customizations needs to go in the same. And what is the purpose of you taking this in grocery crud is first question. Cuz grocery crud is usually an application library preferably useful for building applications like the admin / backend sections. That is where you have major crud operations. This looks more like an independent application in itself..and to achieve the same in grocery crud is possible but with quite an amount of alterations.
If you wish to take the effort, i can guide you on the same..
1 - Wherever you need to have add button, you can give a callback column for each field and generate the necessary textbox with button in it. Now the text fields are the ones where you will be storing / displaying titles (descriptive data) but at the backend you will naturally like to store in id. So you can also pass on hidden field code for the same. (Mind it, you need to follow the norms of grocery crud for the field naming convention)
2 - You can define and add your custom JS and bind the functions to the buttons dynamically. On click of each you can have a lightbox popup as required which will avail you the list as required. On click of the list, you can make the ajax call to update the status of the driver .. and also set the name / id value in the add / edit form through javascript.
If required, you can callback insert to manage the insert yourway .. if required. This is the way you surely can achieve your desired solution.