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I'm thinking about a touring built with just spare parts I have.
I have a rear Alivio M430 9 speed derailleur and Alivio 9 speed 11-34t cassette already. I want to have drops and Sora 3400 is the cheapest 9 speed road shifters I could find. I don't think there is a difference between the cog spacing between road and MTB so it should work if my assumption is true.
Yes, with 9-speed this sort of combination works because Shimano mountain and road rear derailleur actuation was the same until mountain 10 came out.
Yss, this setup will work.
You are correct that the sprocket spacing is the same for Shimano (and SRAM) road and mountain 9 speed systems.
Shimano road up to 10 speed and mountain up to 9 speed derailleurs used the same cable actuation ratio (ratio of how much cable is pulled by the shifter to how far the derailleur cage moves laterally). What this means is you can actually use any of those derailleurs as long as the shifter matches the cassette (and the derailleur has capacity for the size of the cassette of course).
