Yes, it is possible to generate this 'learning curve' with JMP. Scripting this simulation would probably be the best since the sample size is the simulation parameter. You might be able to use a formula with the simulation feature in JMP Pro.
Yes, you should be able to repeat this simulation with any modeling approach. You just capture a measure of the error for the training set and the validation set.
The blog post provides the R script, so you could use it, as is, if you have R installed on the same computer as JMP. A short JMP script is necessary to run R with this script.