Yes.
The bigger it is the faster it seems to sprout. I've let the shell fall off and all before while in the paper towel (not recommending this though), if germed at the same time, putting a seed with a smaller taproot will take longer to sprout than if you had just left it in the bag a bit longer.
When you put the seed in the soil, you don't need to bury it, you don't even need the dirt to cover it so long as you have that bag over still, which again should have water beads. You don't want to bury the seed to far or compact the dirt when you do