The race is important for he look and feel of your map, especially if it is more of a high-end map. Your race decides what voice you hear when an alert pops up. (and possibly the worker idle icon, not sure) So if you are playing a map and you have a hero who is a dark Templar, it will look and sound bad to be the zerg race. Example:
your hero: hi I would like to buy the rune of healing
computer: we need more minnnneerrrallzzzzzz.
your hero: ??
So yeah, its not super important but it would be nice to change.
In fact all alert sounds can be change from within the data editor. Look for alerts. Or you can just disable them and play sounds yourself through trigger. The same goes with some UI element like cursor, race tint color. just look look under race (that's where you get to create your own race). I'm not sure the UI model can be changed there however. They did have model in the previewer