In general I would say they should increase your rate of progress, but I'd also add the caveat that it's somewhat going to depend on your level of experience, the skill of the coach in helping you to improve, and how much you take the information you learn in the private(s) and drill it until it's "yours."
If you are a rank beginner, then the privates will give you more opportunity/experience to execute the techniques correctly while under the watchful eye of someone who knows what the technique should look and feel like and can make the adjustments to your technique needed to make sure you aren't repping incorrect movement patterns.
If you are more of an intermediate they may still focus some on technical issues if you are having them, but generally start to focus more on things like how to best train your skills so they are applicable, strategies for dealing with common issues/different types of opponents, and principles.
If you are advanced the focus will generally focus heavily on principles, timing, "Flow," etc...
Hope this helps.