I did quick test using actions and it seems possible with Export Layers to Files script involved after spliting image and creating Smart Object layers. The problem is in recorded parameters for step to export layers to files because it tends to use hard coded prefix. Even if prefix is excluded it wont work because script will always save only 2 PSD files, Layer 0 and Layer 1. When modal for Export Layers to Files is turned on it does pick document name for prefix and everything seems to work fine, hovewer you must see dialogue and must click on Run and Ok at the end of script. There is and one more problem with Destination when modal is turned on, it picks source folder name for export folder and will export or save PSD with SO layer there regardless of what is hard coded or recorded in action step so you must pay attention and change Destination folder if you want some other folder as output folder. By the way in example below I am assuming JPEG source format with single locked layer.
I do not understand why and what is exactly going on, maybe scripters can solve mistery @c.pfaffenbichler @Stephen_A_Marsh @r-bin