Whether or not this is an issue was being discussed in the PR for SERVER-70444, which is fixing a different problem. From the PR discussion:

"It looks like exitCleanly(code) is the entry point for shutdown, and it calls this shutdown() function that invariants globalInShutdownDeprecated(), and then runs the shutdown tasks. Grepping around for `globalInShutdownDeprecated()`, I see it in the connpoon.cpp code. So I don't think new connections can get in, but an already existing one with perfect timing.... probably could."

My recommendation, if confirmed this is an issue, would be to add a globalInShutdownDeprecated() checks in the FSync code after taking a mutex that excludes other fsync operations from making changes (like the shutdown logic).