MQS contacts have essentially the same crimp profile as DuPont contacts, so if they make an MQS die, then it’d almost certainly work well.
What wouldn’t make any sense is to have a custom die made. For that kind of money, you’d just buy a first-party tool made for those contacts (or that is compatible), like the TE AMPMODU MOD IV crimper I have: it’s not made for DuPont pins, but it works perfectly for them. (I’ve used it for MQS contacts, and it did those admirably, too.)