Generally, yes the higher the number of bits the more precision the DAC.
In order for the difference between a 20bit DAC and 24 bit DAC to be heard by people who can hear the difference, the rest of the circuit in and around it must complement it's level of performance. It is all related to the WHOLE circuit design and performance. Since 24bit is pretty good for audio as I understand, one would expect to find the rest of the circuit is of equivalent quality.
I think the main problem is companies who throw in a some ultra precision parts just for selling sake when in reality they would be hard pressed to prove that their design really requires the more EXPENSIVE precision. Not saying this is the case, but only because I haven't investigated. It wouldn't suprise me in the least to find out they are full of BS about it helping anything noticeably.