Not always. A spectral compressor for example cannot be replicated with a volume controller.
A tape machine that compresses the signal because of how the physical medium
behaves is definitely not automating some volume control.
What an amazing conjecture. Pray tell us how the following audio processors
can be implemented as automated volume controls:
1. equalizer
2. delay
3. convolution reverb
4. odd order harmonic distortion
5. pitch correction
6. subharmonic bass generator