If you run it pre-EQ, then your Master Volume settings should have no effect on the signal sent to the DI. If you run it post-EQ, I believe the Master Volume still has no effect on the DI, but any changes you make in the EQ (boosting/cutting, global filters) will go to the DI, which can impact the DI. For example, boosting everything without adjusting your master volume would likely send a hotter signal to the DI.
But, AFAIK, on the Genz heads I've used, the master volume has nothing to do with the DI signal. On my GBE600, I can turn my master volume all the way down and still send a signal to the board. I can only kill the DI with the mute switch. On a head like the Shuttle, without a DI Level control, you can only adjust the output to the DI by running it post-EQ and boosting or cutting with the EQ or global filters. I'm sure that agedhorse or hasbeen will be along shortly to correct me if I've given any incorrect information.