They can. The most basic reason for headphone amps is that not all preamps have headphone outs - indeed, most don't. Some preamp headphone outs are really quite good (the one on my Linn Kolektor is not at all bad) and you would have to spend a significant amount to improve on them.
On the other hand, some are really bad. This is especially true on many entry level receivers/integrated amps. If you have one of these you really may benefit from spending an extra $200 or so on the used market to get an entry level headphone amp, especially if you are using good headphones. But you don't have to - it all depends how important headphone sound is to you, and how much you want to spend. Beware: if you get heavily into the headphone scene, you can end up spending a lot. :)
On the other hand, some are really bad. This is especially true on many entry level receivers/integrated amps. If you have one of these you really may benefit from spending an extra $200 or so on the used market to get an entry level headphone amp, especially if you are using good headphones. But you don't have to - it all depends how important headphone sound is to you, and how much you want to spend. Beware: if you get heavily into the headphone scene, you can end up spending a lot. :)