Yes, it matters. You want to prevent the speaker from rocking from the motion of the woofer, causing some Doppler shift. Of course this depends a lot on the geometry and weight of the speaker. If a light touch can rock it, at all, it needs spikes.
Speakers on carpet over concrete
My system is current located in a partially finished basement. The floor is thick carpet over a thick pad on top of concrete. Does it affect performance of the speaker differently if spikes are used that pierce the carpet and pad, contacting the concrete below versus removing the spikes and having their "feet" resting on top of the carpet which is also a bit less stable? I'm sure I'm not the only one with a system installed on carpet over concrete. How are yours set up?