Not sure about DSP Manager, but I believe I was using it when I was running a rooted Eclair-based ROM on my Droid. I don't think root access is required in general.
PowerAMP has a fully functional 10-band equalizer; my phone is rooted (CM6, which is Froyo-based) , so I don't know for sure, but I'm fairly certain this feature doesn't require root. As far as I know, it should be possible to implement such functionality into any app, but I haven't done much research into that on the development side.
BTW, dbbarney: Android OS releases are named after various desserts, and are alphabetical. I.e., 2.1 = Eclair, 2.2 = Froyo, 2.3 = Gingerbread. Therefore, my experience using equalizer-equipped apps on Eclair and Froyo (older versions) indicates to me that Gingerbread is not a prerequisite.
EDIT: Messed up the URL tag