You show a emitter follower. You can think of it as having negative feedback, but that's a little awkward. It's easier to think of the B-E voltage being roughly constant. When the load draws more current, it pulls down on E. That increases the B-E voltage, which causes more C-E current, delivering more to the load.
The net result is that the load sees a low impedance source. At first approximation (B-E voltage is constant), the output impedance is the impedance the base is being driven with divided by (transistor gain + 1).
Yes, understanding the few basic single-transistor amplifier configurations, how they work, and their general characteristics, is important if you ever want to be good at designing circuits.