Try this "thought experiment". Imagine an artificial 'subject' who had a perfectly flat frequency response between 2 and 9 hz. In other words all FFT bins between 2 and 9 have the same amplitude. In this case, yes you could estimate the combined filter amplitude between 3 and 6 because you know the FFT was flat.
Now imagine a second artificial subject who had ONLY the flat response between 3 and 6, but who had little amplitude in the 2-3 and 6-9 bands.
You can't make assumptions about a filter output for a different band, without knowing the original raw signal input. The filter LOSES a whole bunch of information when it turns a time series of raw signal values into series of amplitude values.