If the local resource is available on the web server, yes, of course it's possible.
Whether it's desirable is another matter, since filesharing protocols are inherently less secure than a point-to-point HTTP connection.
I would personally set up apache locally and proxy the public URL to the workstation, so it won't waste time timing out a network connection when your workstation is unreachable.
If what you're asking is: can I offer resources on my local workstation on the internet without exposing the local machine to the internet - no, obviously not.
But using a proxy you can restrict access to only the public apache machine; it will forward the data from the workstation to the client without ever giving the client access to the local workstation.