How important is the pre-amp?

I agree with Tvad. There is no one correct answer since our perceptions of sound are all subjective. I have tried both ways a number of times, and always come back to an active linestage. Yes, they all sound different, but they all seem to reveal more depth and nuance to my ears, whereas passives seem to have the edge with faster transients and a somewhat leaner sound.
We need a contribution here from georgehifi.

I also think its the heart of a great system.   I like them stripped down, as few switches and other things in the signal path as possible.   Less is more .....  I dont care about specs or anything other than how it sounds, or doesn't sound like ANYTHING more preferably 

you cannot generalize about the importance of preamps as the contribution of preamps to the system performance is all about context and the resolution of the system.

at modest levels of gear preamps are limitations to performance as they add cables, plugs and mediocre circuits to the signal path. you are better off finding sources with analog volume controls that are capable of directly driving amplifiers (less is definitely more at modest levels). your net performance will be higher for the same investment. i’m over-simplifying things somewhat, but this is mostly how it goes. an exception is where you personally prefer the coloration a particular preamp might bring to what you hear. a matter of personal preference....and not how i like to do it.

past a certain point of gear performance/resolution level preamps start to add dynamics and drive to the music. then the next step is preamp synergy with amplifiers. the top level of preamps are the ones made to be optimized with particular amplifiers. at the cutting edge preamps limit amps and amps limit preamps. the idea is the sum is greater than the parts.

in my particular system i have a great passive preamp inside my MSB Select II Dac. it’s really fine directly driving my dart amps. but my darTZeel battery power active preamp combined with my dart amps is even better. but if i did not have multiple analog sources i would eliminate the dart pre and go naked with the MSB passive pre in my dac.

In my experience yes. 
Specifically, I added a preamp to a system with DAC, turntable and integrated amp.  
I negotiated an at home trial with McIntosh C2600 and it made a distinct difference.  Why, I don’t know. 
Would this experience be true with all preamps?  I don’t know either. 

Some subscribe to the theory that the preamp is the "heart" of the system.  Amplification to simply enlarge what is then presented.  For me, the preamp is vital downstream of the DAC but this is driven by personal taste and I like the sound of tubes between the DAC and SS amplifier.
Does this add some distortion, of course. It also adds dimensionality to what otherwise sounds thin to my ears. We are all different I particularly like a little tube distortion. It *feels* good.