No. Systemax makes PaintTool SAI for Windows only, and there is no Linux or browser version. Krita is the closest free replacement, with the same focus on drawing and a similar feel on a graphics tablet.
PaintTool SAI by Systemax · Photos & graphics · No way to run it
Systemax lists PaintTool SAI as a Windows program and nothing else. The same is true of the SAI Ver.2 preview. No
Mac version, no Linux version, no website you can log in to.
Krita is the usual landing spot. It is free, it is built for drawing rather than photo editing, and its brushes and
tablet handling are the part people praise. What SAI people miss is the lightness. SAI opens in a blink and stays
out of your way, while Krita has far more in it and takes a moment longer to start.
Your .sai files do not open anywhere except SAI. Open each one on the Windows machine and export it as a layered
PSD so the layers survive, and as a PNG for the finished picture. Do that before you reinstall anything.
Your drawing tablet is a separate question to the program. Wacom tablets generally work on Linux without you
installing anything, and other brands vary, so test yours in a live session before you commit.
Free drawing program with strong brushes, layers and tablet pressure support. Heavier than SAI and there is more to learn, but it covers the same work.
Your files: Cannot open .sai. Opens layered PSD, so export from SAI as PSD first.
A general image editor rather than a drawing program. Useful for cropping, resizing and cleaning up a scan, not for painting.
Your files: Cannot open .sai. Opens PSD, PNG and JPEG.
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 PaintTool SAI. Everything else you do can move.