Hi Justin,
From what you have described I believe it is possible however you will need Netweaver SSO 2.0. As you will be connecting to your company network using a VPN connection you should be able to use Kerberos/SPNego authentication. You will then be able to use the devices web browser to connected to the Fiori Launchpad.
You will not be able to use the Fiori Mobile client with this method, I believe that will only work with the SAP Authenticator product.
Regards
Ryan