On a typical laptop there isn't really a line-out. There is a headphone/line-out combined output. At least this has been my experience. But in any case, the point is that there is still an amplifier circuit in addition to the DAC, and that circuit is the problem, more than the DAC. On my MacBook Pro, which has a not-below-par DAC/AMP headphone line-out, the sound is terrible, no matter how much or how little I demand from the amp part of the output. In fact, I have found that I get better sound if I lower the iTunes volume and increase the headphone-out volume. It's a noticeable difference in sound timbre and tonal balance. It still sucks, but it's better. And this is whether I am using AAC files or AIF files (or, presumably ALAC--but I haven't tried that format yet).
So . . . if you have an external DAC--even if it's not theoretically any better than the one in your laptop or desktop--the fact that it is a stand-alone DAC, or DAC/AMP combo, should trump the consideration of the DAC comparison. Plus, inside a computer is probably not the best environment for clean D-to-A conversion, although I don't know this for sure.
Now, there are computers with real line-outs, and in the case of the Macbooks, there is even an optical mini-toslink output available through the same 1/8" port for the headphone/line-out output, and I'm very far from being any expert on this whole world. I'm a rank novice. But, it still seems to me that it isn't a forgone conclusion that a standalone DAC won't make a big difference in your situation.
I could be wrong, of course . . .