Not directly. I tried with PC saves, and doesn't work at all.
Checking Arkham Knight, it's mostly the same hex structure between versions, only the header is what changes drastically. Will try overriding the hex data for the Switch save with the PC hex data, avoiding the header. It may work.
Arkham City has a bigger issue, the header is significatly bigger, so I doubt it would work at all tbh.
Gonna check both games. About Arkham Asylum, Idk since I don't have any save at the moment. I may reinstall it from Steam to check how different is the save hex values.
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EDIT: Nope. Actually, modifying the save with the data totally crashes the program. There's more issues than the header. Don't have the expertise to check all the data and pick out which one would work with the Nintendo Switch version.
I was wondering the same but for the 2 Wii U versions.
I checked this a long time ago along other games like Splinter Cell Blacklist and Assassin's Creed 4: Blackflag. Doesn't work the same as this experiment with the Switch version. Was more hopeful with Arkham Knight since it works differently and under the hood the port should work more or less as an hyper downgraded PC version of the game, but it doesn't work at all. Even PC to PS4 save versions of Arkham Knight don't work, so a deeper investigation about how these saves are written would be needed to convert them between consoles.