I don't have a CC to provide the actual value, but I will chime in that you are correct, Tim, capacitance value does matter, with caveats.
Most capacitors on the logic board are what are called bypass capacitors. They sit with one terminal on the voltage (supply) plane, and the other terminal on the ground plane. Under normal operation, they are charged to the operating voltage of the supply plane to which they are connected. So a bypass capacitor tied to the 5V supply plane spends most of its life at 5V, one tied to the 12V supply plane is at 12V, etc.
On the analog board, some capacitors will be bypass capacitors to smooth the output of the voltage supply circuit. But others will be involved the timing of the video circuit or sound circuits, etc.
For bypass capacitors, if the voltage supply dips below the supply voltage, suddenly the capacitor is at a higher voltage than its terminals. So it discharges some of its stored electrons into the board to equalize the voltage. This has the effect of raising the supply plane voltage and lowering the capacitor voltage.
Similarly if the supply plane goes too high. The capacitor absorbs some more charge to raise its voltage and lowers the supply plane voltage.
Obviously, if the power supply stays too high or too low for a long period, the capacitor can't fix that, but for brief excursions, the capacitors smooths things out to an average.
Capacitors with high capacitance are slower to react to changes in the supply voltage, but have more capacity to compensate.
Capacitors with lower capacitance react faster, but have much smaller capacity to affect the overall voltage.
So big 47uF caps are there to smooth out larger, lower frequency excursions. Tiny picofarad range caps (the ceramics we usually ignore) are there to balance out very high frequency but tiny amplitude excursions.
As you might guess, for bypass capacitors, changing the capacitance by 20 or 30% will not have a large effect on the steadiness that the supply plane sees. Likely, the capacitors have a rated tolerarance in the 20% range (meaning a 47uf might be between ~38uF and ~56uF.
But, if the capacitor is not a bypass capacitor, then the actual capacitance may matter a great deal. The timing of some circuits depends on the value of some R (resistance) times the capacitance, and if you change the capacitance, you change the time constant and can affect anything from whether the circuit works at all (timing too far off to coordinate) to the frequency of the sound you're hearing out of speakers.
