Once you had registered them, yes. And even if the router is down, too.

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Sony president Shuhei Yoshida answered some questions regarding PS Vita remote play, more details inside………When people were asking questions regarding whether you need an active internet connection to use remote play Yoshida clarified:Shuhei also added that you can choose between the router connection or direct.“You can choose the best connection in your use case”The Sony president also added that PS4 to PS Vita remote play is hardware based not software based.Source: