Definitely maybe is about the best answer you can get.
It is certainly possible for a virus that runs on one OS to have a payload that can infect files that will run on another OS. If it finds an entire drive full of files that will run on another OS then it may well do it's work there. Many older viruses spread by searching network drives for various executables and inject their code into them, the theory is no different.
The only thing is that the virus will not properly run until you boot into that OS so you may have a window of opportunity to clean up the infection before it fully entrenches itself in the OS. That's also assuming your virus scanner can see and catch all the various payloads the virus may have.
That's not to say all viruses are written to do this though. You may get lucky and the virus is focused on your current OS.
Either way dual-booting is not an excuse to not have good virus protection on both of the operating systems.
Just because Windows is a much larger target for malware and viruses does not mean that other OSes should not protect themselves appropriately.