The perennial question for audiophiles (assuming by "surreal" the OP meant something like "super-real"; I doubt any but the oddest of us would prefer our systems to sound "unreal," "bizarre," "freakish" or any of the other synonyms of "surreal," which originally designates visual art like that of Salvador Dali). No, you don't want reproduced music to be the acoustic equivalent of clocks melting over table tops! So: do you want your system to sound like "real instruments at a live (acoustic) concert"...or do you want MORE than that? This, I presume, is what the OP meant to ask.
Mahgister always brings us back to the fact that perception of sound is a complicated thing involving a lot more than the straightforwardly measurable (that is, the "undistorted"). If that were not true, we'd all like the same equipment—and the same music, too, probably. If measurable accuracy were the gold standard, everyone would prefer solid state to tubes; tubes add distortion. But we often like the "right" kinds of distortion; don't be misled by the seemingly pejorative character of the word.
Having said that, I'll admit to being fond of various kinds of "distortion," despite the fact that I play cello and guitar, my wife plays piano, my daughter violin, and we all play here in our home in the same environment where I also listen to piano, violin and cello as recorded music on my system. Yes, getting timbre right is important. Yes, conveying the scale of the instrument, and its position in space in relation to other instruments in an ensemble—all that is important. But finally, a kind of "super-realism" is often desirable in reproduced sound. Perhaps it compensates somehow for the displacement effect created by the domestic space, which inevitably reminds the brain that it is not actually listening to live music.
Here's a possible analogy to make this point. I used to be a photographer, back in the pre-digital days. I've won awards at juried shows, had my photographs published, etc. I knew what I was doing with a camera. Now, however, I find that I rarely can resist using one or another post-production retouching program for my digital images. I can not only correct for an out-of-true horizon, or crop the image easily; I can actually enhance the color contrast in ways that make the image "pop." Whether you know it or not, most, if not all, published images have been manipulated in such ways. Is that "realistic," "true" to the "original"? Strictly speaking: No. But we often like it better. There's nothing wrong with that. A photograph of, say, an Alpine vista simply cannot capture all the features that make the "original experience" so compelling: the freshness of the air, the sense of grandeur that comes with the sheer physical scale, and so on. So tweaking the photo a bit may trick the brain into supplying some of that missing visceral excitement. The photo is a simulacrum, not a substitute. So with reproduced music.
Despite all this, I agree with tvrgeek about the relative importance of the different elements in the audio chain, no matter what final effect one is striving for: "In order: Source ( fixed, stuck with it). Room (we can do [adjust] within limits). Speakers (pay to play [not sure what this means here]). Electronics (small differences, even ss to tube is small in relation). Tweaks (tiny tiny tiny)."
I've got two systems, both built over many years, both excellent (to my ears), both in acoustically sympathetic rooms. One is "more accurate": I've had PSB Synchrony Ones in there, which measure extremely well; then Von Schweikerts, which sounded a little "better"; now Magneplanar 1.6 QRs, which are the "best" yet. That's my second system. My favorite rig has speakers you've probably never heard of (Scientific Fidelity "Teslas"), which were very badly reviewed by Stereophile when they were made in the 1990s, which pretty much killed them on the market. So be it. They create a more compelling simulacrum of piano, violin, cello—to my ears, which hear these same real instruments in this same acoustic environment daily. They also are more exciting for jazz and rock: better imaging (more than "realistic"), more bass punch, etc. Are they more "accurate"? Draw your own conclusions....