$10k DAC in a 3k system?

Hello all,

Ive owned the same audio rig for 8 years or so (Rega Mira 3 amp> Rega RS5 speakers) 

My source into the Mira3 amp is a headless fanless micro windows7pc I built running jrivermc> musichall Dax 25.3

i am reading some phenomenal things about some of these Dacs in the 10K range ( Chord Dave, Ayre, Lampizator,PS Audio, etc).

My question is a simple one: the other pieces of my system sound great to me, but are at a much lower price point collectively than one of the dacs mentioned above. Do I need to be concerned about my Amp/speakers being fast/dynamic enough to facilitate a Dac like the Dave? Or could I plug a top notch Dac like that into my system and hear the same things I've heard described in the reviews (but on a relative level) ?

thanks in advance for any insight!