The also mention it here https://news.ycombinator.com/item?id=14926851

strings /Applications/Dropbox.app/Contents/Frameworks/libdropbox_watchdog.dylib | grep -i rust shows some hits:

  __ZN14rustc_demangle8demangle17h2ad719809986c0fcE
  _rust_begin_unwind
  /Users/vagrant/client-dropbox-python/dropbox-virtual-env-3985da1e510f-mac-x86_64-10.14/rust/lib/rustlib/x86_64-apple-darwin/lib/libcompiler_builtins-f10e664516557f83.rlib(compiler_builtins-f10e664516557f83.compiler_builtins.7wkmozn8-cgu.0.rcgu.o)
  ___rust_probestack
  /Users/travis/.cargo/registry/src/github.com-1ecc6299db9ec823/compiler_builtins-0.1.5/src/probestack.rs
  ___rust_alloc
  ___rust_dealloc
  ___rust_realloc
  ___rust_alloc_zeroed
  /Users/vagrant/src/client/rust_vendor/hyper-0.10.13/src/buffer.rs
  /Users/vagrant/src/client/rust_vendor/serde_json-1.0.33/src/read.rs
  ...

Looks like they use it fairly lightly though.