Do equipment stands have an impact on electronics?

YES beyond any doubt.  I have generally stayed away from woods no matter how well aged, etc..as my system and others never sounded quite right (to my ears) but that's a personal bias and should not be counted on in any way for anyone else's system.  I have taken the approach of using at least 2 levels of isolation/equipment stands, (1) coarse grade for stability, think heavy duty stands, multi-layer platforms, etc...and (2) component platforms on each stand shelf for full frequency spectrum vibration absorption and dissipation. There are lots of ways and products to go about this; given when I started on this many years ago, the weight of all my components and budget, I found it most effective to go with Adona AV45 line stands and platforms adding Composite Audio platforms over and above the Adona to tick the box on both coarse and fine-grain as mentioned above.  There is still much airborne vibration in the room (at higher SPLs for certain) and from the world itself and the components so I am going to be giving HRS Dampening plates a test in the next 1-2 weeks on all my gear. It should provide the 3 layer of vibration control/absorption I am looking for. That stated there are alot of other fine solutions out there to accomplish all 3 goals...

It matters very much and the higher the level the more it matters.
I have put all electronics on a heavy brick wall (1200kg/m2) and only the speakers are on the groundfloor. The floor is made of 5,5m3 concreet and is floating on 300mm polystyren. By taking the equipment away from the floor the level jumped up at once. After that i experimentet a lot with shelves, haveing diffrent, kinds of quartzsand and led build in the shelves, using birchplywood at lot. I did again help. The idear was that the sand i vibrating and through friktion is turned to heat and away from the equipment.I have also good expirience with ebony both under and also direct on the equipment, inspired by Shunk Moon.
Then all dampingacessories started and after many kond of difrent manufacturs i ended in the Stillpoint line, Universal => Ultra SS=> Ultra 5 where i stand now, the are very good. Even the powerdistributor gains from standing on a Ultra 5. They to reacts very much in relation to what you put under them.
Next step will probaly be the Ultra 6.  Dampingvibration in equipment is a abselute must but also your windows give a lot eve n if you have the special ones with heavy argongass and 4 and 6 mm thick glass.
Nice lisining

I am a firm advocate for isolation

it has made a large difference in my system

when you get it truly right individual sounds are isolated, transparency enhanced, low level details  and imaging articulated and with no changes in tonality

the electronics are not being stressed by resonance

this occurs in both tube and solid state equipment

where you hear this is in detail and separation of instruments, with no smear and decay in time. There is a strong sense of silence between notes, natural decay and sharp attacks

One way you can hear this nicely is on a full swipe of a pianists hand across the keys or fast articulated playing with distict quick gaps between notes. The notes will sound out distinctly without overlap.

it real is like a veil removed in a time sense
things jump out ar you by their lack of resonace and enhanced separation 

I have found two major products that have taken isolation to a great level in my system.

Silent Running Audio racks and isobases and Daedalus DIDs - Daedalus Isolation Devices footers.  

Silent Running Audio is serious isolation.  I have their Craz rack and a number of their isobase platforms.  Kevin Tellekamp works on contracts dealing with precise control of  resonance with the US nuclear submarines and with other groups including demanding micro level medical applications.  

The Craz rack contains an indo-skeletion of titanium, custom material shelves and is a major investment, but it will make a huge difference and will be the last rack you ever buy. It is a work of art - very substantial..

you can also buy SRA isobases  that go on any rack shelf or on the floor commonly with monoblocks. SRA custom makes each shelf to your specific equipment.  My turntable base was designed around my Gavia Galibier and is a thing of beauty. Everything comes wood crated.

the bases come in three grade levels

http://www.silentrunningaudio.com/home.htm

http://www.silentrunningaudio.com/AudioIsolationReviews/sra_reviews.htm

another isolation device that is garnering great attention is Lou Hinkley at Daedalus DIDs - Daedalus Isolation Devices.  Lou who build's exceptionally crafted hardwood speakers has come up with isolation footers that work very effectively.

http://daedalusaudio.com/DiD.html

I have utilized these on my Billy Bags digital rack and they provide enhanced resolution, transparency and isolation with no changes in tonality.  Lou's comments -  Resonance control is crucial in the design of great speaker systems, and now we have applied that knowledge to isolation devices (footers) for components. These devices utilize dissimilar materials to dissipate resonance coupled with bearings to also isolate the electronic component from vibration. Precision made of highly polished billet Aluminum, solid Cherry and Brass with steel bearings.

   Lou has been effectively bringing these to audio shows and demonstrating their impact by adding them component by component to the system. Then removing as well.  The sonic benefits are very apparent.

Starsound throughout here love it .