There are some issues with the post you link to, which I won't delve into too deeply here.
Your question suggests a misunderstanding of the main point that other post was making -- comparing a transitive verb (終【お】える, "to finish something") with the causative form (終【お】わらせる, "to make something be finished") of the intransitive counterpart (終【お】わる, "something finishes, something ends [on its own]").
If you start with a transitive verb like 習【なら】う or 学【まな】ぶ ("to learn"), and the verb has no intransitive counterpart, then you cannot use the causative of the transitive verb to express anything other than making someone or something do the action of the verb: 習【なら】わせる or 学【まな】ばせる just means "make someone learn something".
You could use the potential form of these verbs to express a sense of accomplishment: 習【なら】えた or 学【まな】べた ("was able to learn") implies that there was some difficulty that might have prevented accomplishment, which you overcame.
(In fact, that's what the 済【す】ませる verb often is in the linked post -- the potential of the transitive verb 済【す】ます. Confusingly, it can also be an alternative form of 済【す】ます as the regular -aseru causative ending added to root verb stem sum-; as with many things in language, context helps clarify.)
In answer to your question:
Is it common for Japanese students to use the causative form of the verb "to learn", when talking about the fact that they learnt something in school?
No, it is not common, nor would it be understandable.