Is it possible to make vegan Yorkshire Puddings?
In a pop over-type batter, the eggs provide a few functions:


Egg whites: protein for structure.  Since the popover/yorkshire pudding is leavened by the protein matrix generated by the ingredients setting and capturing the steam that the wet batter is pushing out, you're going to need something to replace the protein here.  The gluten from the wheat flour isn't going to fully provide the structural integrity you need.
Egg whites: Water.  Egg whites are about 92% water by weight.  This helps make your dough liquid enough to produce the steam needed for the leavening.
Egg yolks: fats for weakening the dough.  The fats in the yolks help keep the dough springy and soft as well as provides a nice richness to the flavor.
Egg yolks: emulsifiers.  The lecithin in the yolk helps to bind the water phase of the batter with the fat phase of the batter so that they don't separate.


So, my suggestion would be to up the liquid in the recipe by a few tablespoons, add a little bit more fat, some powdered lecithin (or other emulsifying agents -- you can get vegan lecithin made from mustard), and some soy protein powder.

You might have to play with the combination of these ingredients, but by replicating and replacing the items the egg provides, you'll be much better suited to creating the popover.

Although, you're not making yorkshire pudding FYI -- you're making a popover.  Yorkshire pudding is a popover created by using the rendered fat from a roast.  A popover is the same type of bread, but made without using animal fat.