I can only offer you a two-part half-answer
1. I have had situations with various distros, where sound did not work for me from the liveCD, but once I installed it the sound worked. So unfortunately, I do not think you will be able to judge purely on the Mint liveCD, but it is a good start. Boot it, and see what happens.
2. If #1 does not work, try http://www.knoppix.com/;
it is a liveCD only (non-installable). It is said to have the best hardware detection. Unfortunately, and this is the half-answer part, if your sound works under Knoppix, I do not know how you find out which (combination?) of drivers is it that got it to work.