Break in for new DAC

Life's a biartch and then you die.

does the amp really need to be on?

Few have addressed this point.  The DAC does push some electricity towards the amplifier, and the amplifier presents as a load to the DAC.  So why not create an equivalent dummy load from resistors just in case electrons really can create a burn-in effect?

I am reminded of a radio skit from John Cleese and others, about a letter to an Agony Aunt in a women's magazine:

Dear Marge

I am worried about my son.  He is growing something in his window box which he says is cabbage, but I think is marijuana.  What should I do? Yours, Worried.

Dear Worried

try some and if you are still worried, it's cabbage

Generally speaking, most equipment needs break-in to sound best, in my own experience.  200 hours or more for your DAC would not seem unreasonable to me, which will happen naturally over time as you use it.  I would not leave the tube equipment on for that long just to burn in the DAC.

"most equipment needs break-in to sound best"

not really, aging (break-in), increases digital circuits jitter/s, negatively impact switches/drives strength.

Every moment a tube component is on, tube life gets shorter. Also, burn in provides no objective sound difference.