Yes. A subwoofer will put out only bass notes. Mid bass will come from your 5.2" or 6.5" or 6x9 speakers. High notes like voices and things of that nature will come from tweeters.
So, you have a $1.5k budget for subs, and you are going to settle for the ones you can get for less than a bill apiece??? That makes absolutely no sense.
What is your budget? & if you want bass, then you will want to get a subwoofer or 2, which requires an amp.
The single best thing you can do to improve your sound quality is probably upgrading your head unit.