My guess for where to look would be to check in the scripts section to see if you can use scripts to do that.
To do it outside After Effects, I would think it could be done in any programming language that can read and write data files (eg. for simplicity, mono, reading and writing with the word length the audio file has for each numerical value). Have one file for the short sound effect, have another file for writing to (the duration of the audio file you are writing to should be approx the same as your composition), and make the file you are writing to have the same sample rate as the other file. For simplicity have the audio files as RAW audio, or use WAV - ie. signed 16 bit PCM, which is RAW with a particular size header. Any time there's no sound, write '0' (ie. zero numerical value) to the output file, every time there's a particle birth (however many times per second you have it set up), copy the values from the short sound effect to the output file. Really, to allow for multiple sound effects in the output file simultaneously, you can add the values from the short sound effect to the output file instead of just copying them (so if there are 2 sound effects being played simultaneously, with the audio sample value from one being "5" and the other being "100", at that point in the output file, you'd write "105" as the audio sample value. Make sure the total doesn't add up to a value that is too high (or too low, since audio sample values normally are negative to positive, with 0 in the middle) - if it does you could just set it to the maximum (or min for negative values) value allowed. For efficiency, you're probably best storing some or all of the file(s)/audio samples in memory (having a buffer to speed it up). After you've finished writing, load the output file into AE or a video editor and use for the audio (or if you've saved it as RAW, convert it to WAV first).
A very simplified version of the above:
1) If the short sound effect file (say it's a RAW file) contains just the following audio sample values "1, 2, 3" (ie. 3 numeric values).
2) The output file could contain (depending on the particle birth rate and required audio duration) the following audio sample values "1, 2, 3, 0, 0, 1, 2, 3, 0, 0" etc. (where the zeroes indicate points where it will be silent).