The Crack is amplifying the output of the DAC, so yes, you will hear the DAC noise floor more through the Crack turned way up than directly from the DAC line level output. If the DAC has separate gain stage for the headphone output then it might still have less gain into your headphones than the Crack.
"highest steps of the attenuator" - are those steps ones that you find a useable listening level, or are they too loud for listening? I'm trying to get a feel for whether this noise is super intrusive, mildy annoying at higher volume settings, or only there when you crank it to the top with no signal present.