Answer
Not as a standard customer-side customization within IEE itself — IFS could build this as a bespoke customization, but there's no supported customer-facing way to add a new button to Shop Floor Workbench in IEE. On the Aurena client (from Apps10 UPD6 onward), this is achievable: you can create a Custom Action, which serves as the Aurena equivalent of adding a custom button to the Shop Floor Workbench experience.