No. XSplit Broadcaster lists 64-bit Windows 10 as its requirement and has no Mac or Linux version. OBS Studio is the free Linux replacement and is what most streamers use anyway.
XSplit Broadcaster by SplitmediaLabs · Video · No way to run it
The XSplit Broadcaster page gives the operating system as Windows 10 64-bit for both minimum and
recommended specifications. Linux is not mentioned, there is no browser version, and a paid XSplit
premium licence does not transfer to anything that runs on Linux.
OBS Studio covers the same ground. Scenes, sources, transitions, a webcam overlay, game capture,
recording to disk and streaming to Twitch or YouTube are all there, and it is free with no
watermark and no premium tier. It is the tool XSplit is usually compared against.
There are gaps to know about. Some capture cards need checking against Linux support before you
buy or move, and a few streaming plug-ins written only for Windows have no Linux build. Game
capture also behaves differently, because Linux desktops hand over windows in their own way, so
expect to redo your scene setup rather than import it.
XSplit scene collections do not import. Write down or screenshot your layouts before you switch,
then rebuild them in OBS. Your overlay images, alert sources and stream keys all work as they are.
For editing the recordings afterwards rather than producing the live show.
Your files: Imports MP4 and MKV recordings from OBS or XSplit.
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 XSplit Broadcaster. Everything else you do can move.