The sound selection is binary number represented by the combination of the solenoid outputs of the Driverboard. You won't get the right sounds without all the transistors in place... Each of the solenoid outputs is one of the digits in the binary number. Without some of the driver transistors, some of the binary digits are locked at "1". They can't be grounded to "0" since the driver transistor is missing. This prevents some of the sounds to be properly selected and a different sound with a 1 in that digit plays.
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Now if I were to put a sound rom from say a Flash into a sound card in a Phoenix, would it make the appropriate flash sounds for the scoring? It wouldn't make the droning sound that increases in intensity obviously, since the Phoenix roms aren't programmed for it, but would it use all the scoring sounds from the Flash, or would the address lines be all messed up?

I depends on which sound "numbers" are used in each game. If one game uses them but another doesnt, moving the card to the one that doesnt will never play the sound.

There are some gotchas that can happen along these same lines but it will probably make noise at least. I use a laserball at the moment to test the rectangle wms type 1 sounds. I think it is Disco Fever software running in laserball will make the sound board look dead just because of how the sound selects are arranged. Whatever signal mutes in disco fever always happens in laserball.

Phoenix uses a different ROM than Flash. If you have the same ROM type / ROM jumpers in both boards then you can move the ROM too.

An example of what could be happening. Lets assume all the transistors are working except the transistor for the 5th binary digit is missing. Since the transistor is not there to switch this digit to 0 or LOW, the digit is locked at logic "1" or HIGH. Therefore, when the CPU is trying to select the sound at decimal 0 (for example) the sound board will play sound 16. Similarly, if it tries to select decimal sound 6, decimal sound 22 will play. Since the 5th digit is always 1 or HIGH, the sound board will never be able to select sounds 0 through 15 and will end up playing sounds 16 though 31 instead.

The opposite can occur if a transistor fails shorted. The digit would be locked at 0 or LOW and it would always play sounds 0-15 and never be able to play sounds 16-31.

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Awesome!