The most acurate answer to the general question is...Depends.
Depends on the type additive. Are you talking an after market additive like Lucas treatment products or additives used in the manufacturing process.
Depends on the lubricant. In heavy gear lubes using a colliodal suspension, yes it will settle out over a period of time but can be re-suspended with a thorough mixing.
Using an analogy like tea or kool-aid. If you add suger to hot tea it melts completely. If left to evaporate a sticky residue will be left. Put sugar in ice tea and not all of it melts. It will settle to the bottom. This is not an exact analogy put makes the point.
Manufacturing engine oils and greases is basically a cooking process. Very monitored temps at specific time frames places additives in a particular order.
If an after market product are the base stock the same? If not over an extended period of time, if not properly mixed then there is a possibility they could separate.
Too many variables exist to answer your question with a definitive answer.