I am setting up my new Roku and it says I have to transfer my subscription management for existing subscriptions to Roku. If I transfer my Netflix and Hulu will I still be able to use them on devices without Roku?
That's the first time I've ever heard of this. Are you certain when you linked your device you went to https://roku.com/link? There's a lot of scams out there, so I'm always suspicious when something sounds out of the ordinary. There's advantages to not having your subscriptions paid through Roku.
I am suspicious as well. But more to the point, if you subscribed to these services directly with these services (and I think that's the only way to subscribe to Netflix) you will want to continue with these current subscriptions if you want to use them with all devices that support them.
I have subscriptions to four paid services (Netflix, Hulu, Prime, Acorn), all made directly with the services, not through Roku, and I can view them on all my devices, including my Rokus. Admittedly I have no direct knowledge of premiums subscribed-to via third party providers like Roku, but I believe these would only be viewable via the third party provider - someone will be glad to jump on me with both feet if this is wrong.
The only way I can envision needing to move a subscription would be if you made it through a third party provider like a cable or satellite company and you no longer have that cable or satellite account and can no longer view the channel.