Azure ADDS and on-premise file server permissions

Hello!

I need some guidence regarding Azure ADDS and on-premise servers.

I have a customer that is using Office 365. Currently only for e-mail, Skype for Business and Office applications. They also have an on-premise file server and some  other application servers, but no local Active Directory. 

Currently they logon with local computer accounts and access file server shares using local accounts created on the file server.

The customer want to use their Office 365 accounts to login to their computers and access shares on the file server with the same account. Is this possible? I've been searching for this and found a couple of different forum threads but no definitive answer.

TLDR;

Would it be possible to setup Azure ADDS with Express Route or VPN to the customers network, join the on-premise servers to Azure ADDS and set permissions to folders/files for the Office 365 accounts on the on-premise servers?

Thanks in advance!