You can grab SOME, depending on your STR and just how much loot, Armour and Weapons you are willing to drop.
It's hard, but not impossible. Youneed a high sneak skill, and/ or items which improve your sneak skill. Look up videos about it on youtube on how to sneak past Elijah. But, you don't need very high strength to do it, just a high sneak level, and the perfect timing
You should watch the video of 'culveyhouse' about it on youtube, he explaines it very well, it is his dead money walkthrough part 42.
The room that Elijah comes from, the one he retreats into if he spots you, there are two entrances, one immediately to your right as you come out of the vault, and one to the far upper right. You need to take the quickest route to that door immediately after you exit the vault, and about half way or 3 quarters of the way(not sure when its necessary) you start to sneak. Not really sure if the sneaking is necessary, just know thats how I saw it done.
Well it was meant not to be possible after all the point of this DLC was. Dont be to greedy. You could lose your life.
STEP 1: Save every frag mine and gas bomb you find.
STEP 2: When you are in the Vault, lay as many as you can on the small stairs nearest the area with all the gold bars.
STEP 3: Go into the room with the gold bars, pick ALL of them up. You won't be able to run, but that doesn't matter. Listen to Elijah's BS, convince him to come downstairs.
STEP 4: The moment you can get out of the room, trudge all the way to the place you laid all the mines. Their should be a hologram wall blocking you. Elijah will come out, go to the wall, and say "did you really think you could steal from me?" and all that shit.
STEP 5: He will activate the turrets. Push up against the hologram wall to the left, and destroy the turrets.
STEP 6: STILL AGAINST THE HOLOGRAM WALL, Elijah will get pissed, and come out to kill you. You WILL glitch, and be thrown inside the hologram wall. Elijah will explode from all the frag mines, and activate the countdown. Normally, you'd have to go all around the vault to escape, and die, but now you can just walk to the elevator, free and clear.
STEP 7: Exit the DLC, trudging along to the gate. Back in the Mojave, unless you have the long haul perk, put the gold in the equipment storage box.
STEP 8: BE RICH!
Don't forget that for it to work you need to have the option to sneak past Elijah for all of these to work. If it doesn't say sneak past just confront then Elijah will put up the security doors. I found that out the hard way. You can also sneak past him by going through the way he takes but it is a bit hard. If it doesn't say sneak past reload a save and check with skill check leads to a sneak option.