No. GOG say Galaxy is available for Windows and Mac only. Your GOG library still works on Linux through Heroic, which supports GOG officially and does the same job.
GOG Galaxy by GOG · Gaming · No way to run it
GOG's own Galaxy page states the launcher is available for Windows and Mac, and there is no Linux download.
That has been the position for years.
Heroic Games Launcher is the answer most people use. It is a free open source launcher for Epic, GOG and
Amazon Prime Games, it runs on Linux, and you sign in with your normal GOG account. Your library appears,
you press install, and Windows-only games run through a compatibility layer without you setting one up.
Lutris will also manage a GOG library if you prefer it.
GOG games are famously free of copy protection, which is why this works as well as it does. A good number
of them also have proper Linux versions that GOG hand you directly.
Your purchases are permanently yours and nothing about them changes. Cloud saves, achievements and the
friends list are the parts that sometimes lag behind the official launcher.
For running a single GOG installer as a Windows program rather than managing a library.
Your files: Works with GOG's offline installer files, which have no copy protection.
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 GOG Galaxy. Everything else you do can move.