Yes. You control three triggers that trigger at the same time (draw, ichorid, nether shadow), you choose the order they go on the stack. Note that only those three triggers will trigger this turn; additional Ichorids or Nether Shadows won't trigger even if they make it to the graveyard before anything other than Bauble's draw effect resolve.
Edit: I missed something critical here that Katzby pointed out to me.
Nether Shadow {BB} |Creature -- Spirit| 1/1. Haste / At the beginning of your upkeep, if Nether Shadow is in your graveyard with three or more creature cards above it, you may put Nether Shadow into play.
Nether Shadow has what we call an intervening if clause. Nether Shadow's trigger will not go on the stack if it is not in the graveyard with 3 or more creature cards above it, and if that condition is not true when the trigger resolves it will do nothing. So here, Nether Shadow will not even trigger or go onto the stack, and we only have two triggers on the stack: Urza's Bauble's draw trigger and Ichorid's trigger.