Change of Duplicati server (+ OS) without losing the remote data gets into path and permission issues. Basically a Duplicati backup keeps one type of paths. Don’t change your mind. Other things are easier.
Whether or not you care about things such as restoring NTFS ACLs and Linux permissions is your call, however if you want them without conversion risk, then I think the OS on its own filesystems does best.
Easier is if you simply want the file content. I think Linux can often read/write NTFS. Reverse is harder. There’s plenty of information on the web about this, if you want to try to set it up for Duplicati. Example:
How to Mount and Access Windows NTFS Drives in Linux
3 Ways to Access Your Linux Partitions From Windows
Are you already doing things like this? If not, then backup of an OS while it’s up might work. What else would change its data when it’s down? Of course infrequently scheduled backups complicate this plan. Scripting a backup on shutdown would solve it, but then shutdown is slower. There are many tradeoffs.
EDIT:
Topic title mentions “restart and login to both”. Why is login mentioned? Duplicati doesn’t need the login, and running it as a service would give another option (e.g. scheduled backup) if a no-login restart is OK.