Yes, but in my experience: Save games are synced to steam cloud and thus are available on Linux and Windows respectively. Settings aren't migrated usually (but sometimes?!), but as long as you didn't tweak them too much, that's not a big deal.
More interestingly: Games that won't start on Linux in this scenario aren't necessarily installed on your windows disk. It's any disk with a NTFS/FAT/exFAT filesystem that seems to cause this. At least that's what my results were, when I tried to set up a shared library between windows and Linux when I used dual boot to facilitate the switch.
It's not that I've been healing 27 times throughout the fight and he only once. It's that I just realized, that I probably need to heal 54 times or more in this fight, but I only brought about 30 potions...