Sounds doable. There's two obvious encessary steps: reading the data from the curves, outputting the audio. The first is not so hard, depending on how the input is described, if it is a black and white image as the one you linked then i would read each column of pixels, in search of the white pixel, the location of the white pixel giving the value (y-coordinate) of the curve at that column (x-coordinate). That's one approach.
For converting the data into audio you'd have to do some research as to how audio is recorded. basically you want to map a sound wave into a sequence of values. Generally speaking audio is recorded by sampling every so often. You have some device, like a microphone, which is sensitive to sound waves. This device encodes its interaction with any sound wave at time t into a value. So if a microphone is exposed to a sound lasting for 1 second, then, if you sample every 1/10th of a second, the microphone will generate 10 interrupts to the computer, in each interrupt providing the value it read at time t. This is they key point, you need to know how the microphone encodes a sample into data, once you know that you can use the image of the wave to produce your samples.
Notice that the sampling rate is usually pretty high. For .wav files the sample rate is 44100Mhz, so 44100 frames per second. Each frame usually having two samples (stereo), or one sample (mono).
This sounds like an interesting project. It would be cool to make a program that converts a curve into the respective sound.