It has to reproduce the range it is capable of correctly...particularly harmonics and overtones, which is what people hear mostly when they talk about the "texture" and "tone" of the bass. Most drums don't go much below 40Hz anyway...only possibly some really big bass ones but again, you are mostly reacting to the upper frequencies when judging whether or not it sounds like a real drum.
depends on how much ambient/venue info is important to you. not always a factor for musical immersion, but sometimes (recording dependent) it matters for the complete picture.