It depends on how the ear was damaged. The cochlea has two types of hair cells: inner and outer. The outer hair cells amplify the incoming sounds by vibrating

It depends on how the ear was damaged. The cochlea has two types of hair cells: inner and outer. The outer hair cells amplify the incoming sounds by vibrating in tune with them, and the inner hair cells actually pass the signals along to your brain. If the outer hair cells get damaged, your ear can still perceive all the frequencies; they just aren't amplified enough. In that case, you're correct that boosting the frequencies back up according to your audiogram (with some nonlinear compression to account for loudness recruitment) can bring back your hearing. The same holds if you have a conductive loss (poor transmission of sounds between your eardrum and your cochlea). On the other hand, if the inner hair cells get damaged, you can no longer hear at the frequencies corresponding with the hair cells that were damaged. The same holds if you damage the connections between the inner hair cells and the nerves, or if you damage the nerves themselves (in which case you may have normal hearing thresholds but still have trouble hearing). In these cases, even if you amplify to match the loss, you can't bring back normal hearing; hence the need for signal processing to make the best of what you have left.