Yes, in fact I did the exact same thing with the same DAC for some time and it does substantially improve on the dac inside the bluesound. If you use a top end coax cable to go into the qutest dac you will get great results. Now looking at your current components you might want to get yourself something better than a vault. I now have an Aurender N100H server/streamer and it is fantastic. I use an MHDT Pagoda NOS DAC and wow...great sound.
Bluesound Vault 2i and a Qutest DAC
In trying to get rid of the thousand physical CDs i own so I demoed the Bluesound Vault 2i against my Theta Miles CD player (with a Krell integrated amp and Thiel speakers.) The Theta produced better sound so I sent back the vault. Someone suggested that I use an external DAC, like the Chord Electronics Qutest DAC, with the Vault 2i to produce the quality of my CD player. Has anyone any experience with this scenario?