Nope, it has it's own opamp (more than one in the case of a decent sound card). If you had a sound card with no opamps, and just line level outputs (there are sound cards like this, mine for example), your speakers would not work without an external amp, unless the speakers have an amp built in, as some computer speakers do.
If you have a line level output then you would want the volume at maximum (+0dB). When you lower or raise volume on a sound card with an opamp(s) the amplification level is simply changed. You can not "lower" the volume of a line level output, because it is already +0dB. When you "lower" the volume of a line level output, since it can not go lower, the digital signal is simply attenuated which causes a drop in bit depth, and lowers that quality of sound.