If I understand it, you have an unusual situation where the speakers are in one end of a room with a suspended floor over the basement, and the components are in the other end of the room over a suspended crawl space. Your concern is whether spiking the equipment rack in the component end would be advisable. Before you can answer that, you need to determine the magnitude and frequency of the room and floor resonances, to see what if anything you need to do.
Here are some ideas for how you might approach this.
1.Measure the room response at the listening and component positions. See if there are large peaks below 120 Hz., as these are the ones with the most energy and likely to disturb your components the most.
2.Feel the floor at these frequencies and see if the floor gets to vibrating significantly at any of them. The floor resonant frequency may be different than the room resonant frequency. Floor resonance will be very noticeable through your feet or bottom, especially at the center of the suspended floor sections.
3.Walk throughout the room while playing music with deep base and listen for peak areas, typically near walls or corners. Put your finger tips on the equipment and feel for the nature and extent of the vibrations being introduced.
4.Record all of these observations.
5.If you are lucky, the room modes will be well behaved and spread uniformly, and the floor will be solid (the component space has 11 ft. floor joists, which if not too far apart may be more than adequate). In this case, the spikes are fine and you will not need to do anything.
6.More likely, you will have both some difficult room modes and some specific floor frequency resonance that can shake everything in the room. Dealing with room modes is a popular topic here and you can find plenty in the archives. The floor also can be dealt with in a number of ways.
7.You can stiffen the floor from underneath as described by Rushton and Sean. My suggestion would be to first place a 4x4 beam perpendicular to the joists in the center of either or both floor areas where the resonant amplitude is the greatest, second, place one under the speakers which are the source of the energy, and third, place one under the equipment rack which reacts to the resonance, in that order. The first one may be enough.
8.If posts are intrusive below, you can eliminate them in favor of adding blocking between the joists (if the basement ceiling is exposed), or take 2x6s and lag bolt them perpendicular to the joists. The 2x6s work very well if the basement ceiling is dry walled and you dont want to disturb it. Start with a single 2x6 in the center of the room. This may be enough without any posts.
9.Repeat 1-3 as you progress. When you quiet the floor it will be obvious to both your ears and the measurements taken. Since the speakers are no longer putting energy into exciting the floor, they will much more quickly respond to exciting the air and sound much tighter. Since the rack is not shaking as much, any shelf damping under components will be more effective. It is a win - win.
10.As you stiffen the floor, you can expect more of your speakers bass energy to get into the listening room and propagate further into the house. This may necessitate more in the way of room treatment, such as tube traps etc.
So this may be the beginning of a longer journey. Sometimes a change for the better opens up a whole string of possible improvements. Only you will know when enough is enough. I hope this is helpful.