An amplifier takes an incoming signal and makes it louder. That's it. It sounds like you needed one, since your headphone was too quiet at your PC's max volume output.

Every single digital audio device on earth (including laptops, PCs, DAPs, iPods, phones) contains a DAC. Otherwise music would sound like this: "11000110010100101010100100001100101"

So the question is only whether a fancy external DAC would sound better than the DAC in your given device.

In my opinion, unless there is audible distortion coming from the device due to a lack of EM shielding or something, the answer is invariably "no."

But opinions on this vary.