You are correct, it's too much of an easy answer. If there are no other sound travel paths, yes. In the real world, however, things are different because sound also travels around the silencer.
I once worked on a machine that was extremely noisy. With a normal (for that company) noise enclosure the sound was about 105 dB. I said to put the machine on vibration isolators, another engineer said to add a second noise enclosure around the first one. I was new there, he was well connected with management, so they built a second noise enclosure over the first. When they measured the noise level at 105 dB, they called me back. Standing ten feet from the machine, I pointed the meter at the machine and measured 105 dB, pointed the meter away from the machine and measured 105 dB, pointed the meter down toward the floor and measured 107 dB. The noise was going under the noise enclosure through the concrete floor. They put in the vibration isolators and got the machine down to the 80 dB called for in the contract.
If the silencer is improved enough, the primary noise source will be something else. It could be noise radiated from the duct, it could be from the fan inlet or outlet, it could be flow noise after the silencer. On the other hand, if the other noise sources are small enough compared the duct noise, then two 10 dB silencers in series will result in 20 dB reduction.
