If they did not put any additive in it then
I WOULD NOT DRIVE IT UNTIL YOU GET SOME! Without any additive at all you can burn out the clutches in the LSD 
the dealer should have never done the job if they didn't have the additive in stock. You can go to your local parts store and they will carry it, it is only like $5 and really easy to put in ( 3/8 ratchet for the fill plug and thats all you need ). BTW did they use a synthetic gear oil or a regular gear oil? Page 323 of your '03 owners manual says you have to run synthetic gear oil ( same as in an '02 ) it also list two different weight gear oils to use one for fuel effecincy 75w90 and the other is a heavier 75w-140 ( which I recomend if you do any towing or hard driving ).
I know alot of people here in the southwest that have gone with the Royal purple from Ford and Dodge diesel trucks to the lighter duty gas vehicles and all have had great performance from the Royal purple ( The reason I changed to it was word of mouth and online research ) but there are also some people who say that they don't trust it alone and will still put in more additive ( which never hurts, the LSD's are expensive to replace ). I had run the Valvoline synthetic gear oil ( which is a good oil ) and two bottles of the friction modifier and still had a slight shudder turning from a stop and even worse when I had my car trailer behind me ( Even unloaded ), when I switched I have not felt one shudder from the LSD with the Royal purple and I am not running any additional friction modifier with it. You will be looking at around $ 60 or so for the Royal purple ( even less if you have a buddy who works at a parts store and gets good discounts )

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Not sure about the diff's in the '02 vs. '03 because the '02 is a solid axle and the '03 is independent suspension, but I would think that the LSD in the carrier is the same. The Royal purple is manufactured with the friction modifiers in it already and will work with all LSD's either plate & clutch or cone type.
This info comes straight from there websight:
http://www.royalpurple.com/gear-oil.html
Max-Gear is an ultra-tough automotive gear oil. It’s designed to maximize power and provide unsurpassed protection to heavily loaded gears. It makes gears run smoother, quieter, cooler and longer without overhauls.
Max-Gear outperforms other gear oils because it combines the
highest quality synthetic oils with Royal Purple’s proprietary Synslide additive technology.
Max-Gear is recommended for use in truck, motor home / RV, and automotive front or rear differentials, manual transmissions, and lower gear units of marine engines that specify use of an API GL-5 or GL-4 fluid.
All viscosities of Max-Gear are formulated with hypoid friction modifiers necessary for use in clutch or cone type differentials. No additional additives are necessary.
Hope this helps

I tried to be as through as possible but if you have any questions shoot 'em at me.