The Alteryx server is like any Web Service, your workflows are run in the Alteryx Gallery (a Web Service) by an account other than yours, because of this the workflows have access to the resources with accessibility granted to the hosting account. Now Googling around I found this article Making your Computer Accessible from the Public Internet which creates security concerns to your organization, I don't like the idea of Web Server accessing clients' work station resources, that's quite dangerous.
When publishing the workflow on your Alteryx Server, we usually use shared folders/drive to which both the server and you can access.
To answer your question, no, the server can't access your local drive.
If you have a batch process and are basically uploading the workflow on your gallery to schedule, a workaround is to use the scheduler inside your Alteryx Designer, which requires additional configuration and help from your Alteryx Server admin.
