I would guess that at the lowest level too much is dictated by physics. It may be possible to obfuscate some higher abstraction layers though.
> Five individual logic cells were functionally disconnected from the rest— with no pathways that would allow them to influence the output— yet when the researcher disabled any one of them the chip lost its ability to discriminate the tones. Furthermore, the final program did not work reliably when it was loaded onto other FPGAs of the same type.
The article says they only image the metal layers, so I guess you can do anything as long as you don't visibly change the metal layers.