How important is the rack you use for your components

As @newbee points out the effect is system dependent. In a more resolving system the impact may be substantial. For example in my system each step in moving my VTL power amps from spiked Grand Prix Audio Monaco stands to Apex (ball) footers and then adding a Marigo sub shelf under the amps was very noticeable.

The general effect of reducing vibration on an amp is to make the amp sound less loud (ie for a given setting of the volume control you hear less harshness and hence can afford to dial it up a few notches) and give greater control over dynamic peaks and hard to resolve passages. Impact on source components can be similar but more diverse. Turntables are another story entirely and need their own isolation solutions.

IMHO an audio rack's contribution to audio is in improving control of the effect of vibrations on the components either in dissipating them (the vibrations) or isolating them (the components). Much of the effect is component dependent - turntables, tube equipment, might benefit the most, solid state stuff , not so much.

 Probably for many the effect for using any particular rack is not 'marked', just more aesthetics, or those who are concerned with obtaining some apparent compliance with audio theory. 

I should mention however, that the size of the rack or its configuration and placement can effect the sound your system generates. For example the size and configuration of a rack between the speakers places a far larger roll in the systems sound than when the rack is on the side walls or the back wall. But to make that a little complex, the lengths of cables or IC's (and the type of cables and IC's) can be a large factor in your systems sound. 

Lastly, what is 'marked' for a deaf man is significantly different than what is 'marked' for an anal audiophile. What I personally concern myself with is keeping the critical components out of areas where there are typically bass nodes. The side walls work best for me, or when limited, placed between the speakers but out from the back wall several feet because there I can keep all my wiring short minimizing the their effect.

To your question - important yes, marked (as in big) not so much.