No. NVIDIA lists the app for Windows 10 and Windows 11 only. The graphics driver itself is on Linux and works well, but the app around it, including ShadowPlay and the game settings, is not.
NVIDIA app by NVIDIA · Utilities · No way to run it
The NVIDIA app, which replaced GeForce Experience, requires Windows 10 or Windows 11. Linux is not on the
list and NVIDIA has not said it will be.
Your card is still properly supported, and that is the part that matters. NVIDIA writes and publishes its own
Linux driver, kept at the same version numbers as the Windows one. On the beginner distributions you turn it
on from a drivers settings window rather than downloading anything, and after that driver updates arrive with
the rest of your system updates instead of through a separate app.
What goes missing is everything the app wrapped around the driver. ShadowPlay game recording, the automatic
per-game settings, Freestyle filters and the built-in performance overlay have no NVIDIA-made Linux version.
OBS Studio records and streams gameplay and is what Linux users install for that. MangoHud draws the
performance numbers over a game. Game settings you set inside each game yourself.
Nothing of yours is stored in the app. Recordings you made with ShadowPlay are ordinary video files and play
fine on Linux in VLC or mpv.
Replaces the in-game performance overlay. Fiddlier to switch on, and it does not adjust any graphics settings.
This doesn't have to stop you
One stubborn program doesn't have to decide the whole question. You can keep Windows on the same PC and restart into it only when you need NVIDIA app. Everything else you do can move.