No. Capture One's own system requirements list Windows 10 and 11 and recent macOS only. There is no Linux build and no browser version, and tethered shooting has no free equal on Linux.
Capture One by Capture One A/S · Photos & graphics · No way to run it
Capture One's system requirements page names Windows 10 64-bit 22H2 through Windows 11, and macOS 14
and newer. Linux is not on the list and the company has not indicated any plan to add it. Your
licence is tied to those two systems.
This is one of the harder switches in photography. For plain raw developing, RawTherapee and
darktable are genuinely good and cost nothing, and both read the raw files from your camera. What
they do not match is Capture One's colour handling out of the box, its layers and its speed on a
big shoot.
Tethered shooting is the sticking point for working photographers. Capture One shooting straight
into a session on a laptop is the reason many studios pay for it, and no free Linux program does
that as reliably across as many camera bodies. If tethering pays your bills, keep a Windows or Mac
machine for shoot days.
Your files are safe either way. Raw files, JPEGs and TIFFs all open on Linux. What does not travel
is the editing. Capture One stores its adjustments in its own catalogue and session files, and no
Linux program reads them, so export finished JPEGs or TIFFs of anything you care about before you
move.
Handles the library side that Capture One sessions gave you, including ratings, keywords and search.
Your files: Reads ratings and keywords written into files or XMP sidecars. Does not read Capture One catalogues.
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 Capture One. Everything else you do can move.