I'm not familiar with using it to restore cases, but using solvents to chemically "weld" plastics is a common practice. It is the same process used to build plastic model kits.
Basically you need to figure out what type of plastic is used and then find a solvent that works for that particular plastic without causing too much damage. Not all plastics will work well with all solvents. I am not overly familiar with acetone for this particular purpose, the Plastic "glue" I use for model building and other primarily polystyrene and ABS Plastics is from MEK (Methyl-Ethyl-Ketone, or Butanone).
The way it works is, that the solvent is dissolving the surface of the plastic where its applied until the solvent evaporates. While the plastic is slightly dissolved you press the two pieces together so when it solidifies the two pieces become bonded. It is not so much gluing as chemically welding the pieces together.
To get the best results you have to apply enough solvent that the surface gets a goo like and sticky texture before you press the pieces together to get a better bond. After pressing them together fixate the pieces for some time until it solidifies. Make sure the pieces wont shift. It is not an immediate bond like with superglue and you can't simply clean the glue off and start over.
Usually you will get some plastic squeezed out between the two pieces that you will have to clean off. That is actually the material the "glue" dissolved and not the "glue" itself. To do that use sharp knives, files or sand paper, whatever you need to get the surface texture you want.
The Problem is that not all plastics react the same with any solvent. To see if it will work test the solvent either on sample pieces or apply a small amount to a spot that is not normally visible to see if it will work properly.
If you have never done any of this, it is best to play around with some disposable plastic bits to get a feel for the process.
Also, it should be self explanatory but just in case, the solvents are EXTREMELY flammable, and the fumes are not exactly healthy either. So, keep away from flames and heat sources and do it in well ventilated area. technically I think you are supposed to use gloves, but I know nobody who does that in hobby applications.