That’s the idea, in theory. But because analog components such as the resistors, capacitors, and transistors will not be identical[0] between the master and player, it’s not perfect.
[0]: you can get very low tolerance resistors and capacitors, but they’ll cost you
To a point, but remember that you're dealing with low-bit floating point math. That boosting stage creates information that wasn't originally there. That's not so bad in the treble case where original * boost / filter is pretty close to the original. But in the bass case, original / filter * boost might be significantly different than the original. That's usually not a huge problem because the low bass frequencies are pretty forgiving, but it's something to consider.
If they were idempotent, yes. But they're not. Analog processing can't be perfect, and amplification is an inherently noisy process. The RIAA curve first cuts the signal on the bass end of the spectrum, throwing away information in the process (because vinyl doesn't have infinite resolution). Then it amplifies that degraded signal.
You can simulate this pretty well with computer speakers. Turn down your audio outputs so that it's barely audible, then turn up the speakers as load as they'll go. Noisy, isn't it? In theory that should be the same as turning the outputs to their maximum clean level and turning your speakers way down, but in practice it's absolutely not. Well, every vinyl record made does exactly that to the bass.
Sounds like if you combine the two steps you end up with the identity operator :)