Easily detected.
> sharing it as a document via Dropbox or similar
If you use a TLS-inspecting proxy/VPN, this will be detected. Otherwise, it depends on how much monitoring is going on, but at best they could suspect it.
> Copying to physical storage?
At my work, USB drives are disabled by MDM.
You could use transfer the files over SSH. Even if you have an MitM SSH-inspecting VPN, once the SSH channel is established, you could tunnel a second SSH connection through the established insecure SSH session.
Even then, with enough logging, you could detect that all local files were accessed sequentially which would raise a red flag.
There's nothing you can do to prevent insider espionage that wouldn't raise false positives and block legitimate work, but you could at least detect it.
If any infosec experts feel like chiming in I'd love to learn more.