An amplifier could output 100 milliwatts of power into 600 ohms or 1000 milliwatts into 600 ohms, Just specifying that it can drive 600 ohm headphones is not enough. that , and there is also another factor called the sensitivity. For instance, Planar magnetic headphones have low impedances, but they are very difficult to drive because they have low sensitivity.
Anyway, You can try to see if your sound-card can drive your headphones properly. but if I were you I would buy an amp also. or maybe a DAC/AMP combo.
With a DAC/AMP combo, you can use your sound card's optical out into the DAC/AMP, that way you get the signal processing of your sound card and the superior performance of the DAC and AMP section of your combo.
the DAC chip used in your sound card is pretty decent, the CS4398 is a popular chip.