Yes, unless things have changed since my last warlock multi-class (and from what Luckmann says they haven't), we can choose what level spellslot to use, so if our warlock spellslot level is currently higher than any spellslots we have from other classes we can choose to use warlock spellslots first just by choosing to cast a spell at that level. But when we have "normal" spellslots at the same level as our warlock spellslots the former always get used first and we can't pick. Though as the OP said, given there don't seem to be any circumstances in which it would be sensible to use the non-warlock spellslots first, we don't actually need to choose just reverse the default order.
