First, as an out-of-state resident you can PURCHASE anything that is allowed under the law in the state where the gun show is located.
The big HOWEVER is that you cannot take possession of a FIREARM yourself. For ARs, this also includes lower receivers, since they are serial-numbered as firearms. The general rule is if the purchase requires you to fill out a 4473, then you can't take delivery. Instead, the seller must ship the item to an FFL in your home state. You then pay the home-state FFL a handling fee and take possession from him.
Anything else (uppers, mags, etc.) can be bought and given to you on the spot. The second HOWEVER is that if your home state has banned any of your purchases -- for instance, California's high-cap mag ban -- and you take them home to California, you are illegally importing them to your home state and face prosecution.
HTH.