In short, yes.

From the sources we have available to us concerning his time spent on St. Helena, we know that Napoléon spent much of his time and effort arguing with Sir Hudson Lowe (the governor of St. Helena and, as a result, his warden) about the conditions of his imprisonment - primarily the poor condition of his residence (Longwood House), his meagre allowance (which barely allowed him to pay for repairs on Longwood House, which had fallen into a state of disrepair before his arrival), and the freedoms and privileges he had access to while imprisoned. Though many of his grievances concerning his imprisonment were justified, Lowe proved indifferent towards them, something which Napoléon and his followers resented. Towards the end of his life Napoléon accused Lowe, and the British government at large, of hastening his death due to forcing him to live in unacceptable conditions.

On top of his campaign to improve his imprisonment conditions, Napoléon also authored a biography on Gaius Julius Caesar entitled Précis des guerres de César (Chronicles of Caesar's Wars) and, under the tutelage of the Comte Emmanuel de Las Cases, learnt and studied English - as Lowe prohibited Napoléon's access to French books and newspapers. Other than these pursuits, Napoléon generally spent his time interacting with his various followers who accompanied him in his exile as well as mingling with locals living on St. Helena; most notably the Belcombe family, whose teenage daughter - Lucia Elizabeth Balcombe Abell - he had befriended and would often have picnics with.

Generally, Napoléon spent his time on St. Helena in quiet exile. Though he consistently clashed with Lowe concerning the conditions of his imprisonment, he never seriously attempted to escape his exile; he seems to have been generally resigned to his imprisonment.

Hopefully this answer is helpful, and, as requsted, here's some sources (both primary and secondary) that detail Napoléon's exile in St. Helena:

Sources (Primary):

Balcombe Abell, Elizabeth. Recollections of the Emperor Napoléon. Cambridge: Cambridge University Press, 2017 (original publication 1846).

Bonaparte, Napoléon. Chronicles of Caesar's Wars. Prefaced by Louis Joseph Marchand, translated by Arshan Barzani. London: Clio Books 2017 (original publication 1836).

Emmanuel-Augustin-Dieudonné-Joseph de Las Cases. Mémorial de Sainte Hélène: Journal of the Private Life and Conversations of the Emperor Napoléon at Saint Helena. London: Colburn and Company, 1823.

Sources (Secondary):

Abbott, John. Life of Napoléon Bonaparte: A Life. London: Harper and Brothers, 1883.

McLynn, Frank. Napoléon: A Biography. New York: Random House Publishers, 1998.

Hibbert, Christopher. Napoléon's Women. Sydney: W. W. Norton & Company, 2003.