Amp frequency requirements for super tweeters?

I have become intrigued with discussions of the reported improvements to system sound afforded by the addition of super tweeters- specifically the air and coherence. Being in my late ‘50s, I am less concerned about the frequency extension and more concerned about how it affects what I can hear. My question is this- my amp goes to 20kHz, do I need an extended frequency range amp for driving this?
Same question for digital crossovers like the DCX2496.