What type of "shampoo bar" are you thinking about?
If you mean a bar of lye-based soap for washing one's hair, then yes, the hair should always be rinsed in an acidic solution to help the cuticle of the hair lay back down.
Bear in mind that not everyone's hair responds well to being washed with lye-based soap whether the soap is in liquid or bar form. Some people's hair does okay, but some does not due to the high pH of lye-based soap. An acidic rinse (speaking from experience) slows down the accumulation of damage, but doesn't necessarily eliminate it.
If the bar is a syndet cleanser that's formulated to have a lower pH that's more compatible with hair, then, no, an acidic rinse isn't needed at all.
The issue here is the pH of the cleanser -- it doesn't have anything to do whether the cleanser is "emulsified" or not. Can you explain why you think emulsification is important?
I have to say I'm seeing a fair number of posts lately from people who want to mix emulsifiers with lye-based soap. I'm not sure why this topic is a trending issue. It doesn't make a lot of sense to me at the moment, but I haven't researched it either. If you have a link to a source that is promoting this idea, I'd appreciate learning more.