No. NVDA is a Windows program and there is no Linux version, and running it under Wine does not work. The screen reader on Linux is Orca, which is also free.
NVDA by NV Access · Accessibility · No way to run it
NV Access builds NVDA for Windows only. Its own requirements say 64-bit Windows 10, Windows 11 and
Windows Server from 2016 onwards, and there is no Linux build, official or otherwise.
The obvious hope is Wine, the compatibility layer that runs some Windows programs on Linux. It does not
help here. The request has been open on NVDA's issue tracker since 2019 and the answer has not changed:
NVDA does not run under Wine, and the project has ruled out a native Linux version. Even if it did start,
a screen reader running inside Wine could only see Windows programs running inside Wine. It could not read
your Linux desktop, your settings, your file manager or your login screen, which is most of what you need
read.
The replacement is Orca. It is free and open source like NVDA, it does speech and braille, and on GNOME it
is part of the desktop rather than an add-on. It is not NVDA. The keyboard commands are a different set,
there is no add-on store of the same size, and there is no scripting language to force a stubborn program
to cooperate. App coverage is narrower too: Debian's accessibility documentation says outright that not
every program built with the common Linux toolkits is readable even with accessibility switched on.
None of that is a reason to be talked into or out of anything. It is a reason to test. Run Orca from a live
USB session, on your own machine, with the programs you use every day, and find out what speaks and what
stays silent before you change a thing on your PC.
Free and open source like NVDA, with speech and braille. The keyboard commands are different and app coverage is narrower, so allow real time to relearn it.
Your files: NVDA add-ons and configuration profiles do not transfer. Orca settings are set up from scratch.
NVDA's built-in synthesiser and the default Linux voice are the same family of software, so the sound of it will be familiar.
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 NVDA. Everything else you do can move.