I put a sprinkling of coarse sugar on top of a pie crust that's been brushed with egg, to crisp it a little. Can I put a sprinkling of the coarse sugar directly in the pie pan before putting the bottom layer of crust in it, to give a little bit of crispy bottom crust when baked?
I'd be afraid of the sugar caramelizing and burning on the bottom with the direct and increased heat from the glass or metal pan you are baking in, combined with any trapped moisture coming off of the dough, you will likely end up with a burnt caramel on the bottom, trapping your pie in the pan. [long story short, it depends on the moisture of the dough, the oven heat and baking time, etc]. I wouldn't recommend it.
it works on top because the excess moisture has somewhere to go, and is probably in or just above the oven temperature as opposed to the scenario listed above.
to achieve a crispier bottom crust, perhaps brush the bottom of the pan lightly with melted butter, essentially "frying" the dough as it bakes, or possibly increase the amount of sugar in the actual dough. Alternatively, maybe start off at a really high temperature with your pan on the lowest possible rack to encourage quicker baking/browning.