I am experimenting with growing a few seedling mandarins pretty much unprotected in my yard, I have noticed all the leaves on the upper branches have frozen off, but stems and lower leaves are doing well.

Is there any evidence to support my theory that I may be able to grow these (and possibly other citrus) as a die-back bush and get some kind of crop eventually?

I know some types of trees can adapt to a bush/hedge form, but I've never heard of citrus being grown this way.

I grow all of my trees as bushes. Limbs are touching the ground and they produce a lot of fruit. Some have a natural up right habit but I still dont trim the low limbs.

I am no expert but, since these are seedling trees, the major concern is that the trees may never reach the mature node count required for fruiting. Mature node count is not a count of the total number of nodes on a tree. Rather, the node count at any point on a tree is a count of the nodes along a single path from that point on the tree to the base of the trunk. The idea is that fruit can only be produced at nodes whose count number is greater than the mature node count. A seedling tree grown as a bush may have many branches and nodes but no mature nodes. The mature node count varies from one variety to another. Mandarins have one of the lower mature node count requirements but not as low as key limes or a few others. Seedling trees are often easily distinguishable from grafted trees because the seedling trees only have fruit in the upper part while grafted trees have fruit everywhere. It is possible that your trees may eventually grow enough nodes horizontally on lower branches that those branches may fruit.

You may want to consider grafting some mature scions onto your trees and protect the bud union when it freezes.