We have to care because we play better when we are happy with our sound. The bands I play in would notice but even if they don't know why, they will still appreciate better playing (from a happy bass player).
Some audiences will notice the good stuff. I have guys come up from the audience and ask about 5 string basses and compliment my sound, but that's probably the demographic of the bands I play in. Older music fans might understand a little more? Of the very few younger people who have come up to chat most have been musicians themselves.
IME in the better bands, what and how you play gets you the gig, not what you sound like.