The image of a face glowing from learning Torah is based on Shemot/Ex. 34:29-35, in which Mosheh’s face is radiating light when he comes down from Har Sinai after receiving Torah. But atop Har Sinai, Mosheh did more than “receive.” He was immersed in God’s Presence to the exclusion of all else. Consequently, learning Torah became likened to being in God’s Presence, just as Mosheh had been.
Does learning Torah bring spiritual enlightenment?
There are times when it has:
His face shone like the light of the sun and his effulgence beamed forth like that of Mosheh, so that no one knew whether it was day or night.
They went [outside] and said to Rabbi Yochanan, ‘Come and see Rabbi Eliezer sitting and expounding, his face shining like the light of the sun and his effulgence beaming liked that of Mosheh, so that no one knows whether it is day or night.’
He came inside behind Rabbi Eliezer and kissed him on his head, saying to him, ‘Happy are you, Avraham, Yitzhak and Yakov, because this one has come forth from your loins’!” 
She called to him, ‘Old man! Old man! Are one of the following three things true about you? Are you drunk? Are you rich from lending money on interest? Or are you a swine farmer?’
He answered, ‘I swear that none of these three things are true about me. I don’t loan money at interest because it says in the Torah, ‘Don’t charge your brother interest when you loan him money.’  I don’t raise pigs because it’s forbidden for a Jew to raise pigs. I’m not drunk, since I only taste wine when I make Kiddush on Shabbat, and Havdalah after Shabbat, and when I drink the four cups on Passover.’
‘So then why does your face shine?’ she asked.
‘It’s Torah that lights up my face, as it says, ‘A man’s wisdom lights up his face’ .” 
If that was categorically true, then everyone who studies Torah would be spiritually enlightened or progressing in that direction.
Has that been observed?
We can think of many brilliant minds who have learned and taught Torah, but were they all spiritually enlightened? If so, I would argue that there would have been no need for the development of Kabbalah or Hasidut.
Much depends on why we learn; our intention in learning.
We see a parallel process in practicing Hatha Yoga (yoga postures).
When I was first introduced to Yoga, it was presented as a spiritual practice that can bring personal peace. Yoga postures were meant to quiet the body and mind in preparation for meditation. The people that sought out those yoga classes were motivated for spiritual growth.
Years later, different yoga sites opened, offering yoga as a type of exercise that can improve calmness and flexibility. If people who took part in those classes wanted the physical benefits without the spiritual component, that’s what they got.
Rabbi Morris Lichtenstein similarly compared “prayer” with “suggestion.”
By “suggestion,” he meant “auto-suggestion,” a practice based on Dr. Emil Coué’s having his patients say “Every day, in every way, I am getting better and better.” This was a well-known healing method a century ago. It produced beneficial results, but assumed that it was the human mind or human action that produced those results.
By “prayer,” Rabbi Lichtenstein specifically meant “affirmations” or “visualized prayer,” in which a positive statement or positive mental image is repeated, as in auto-suggestion. However, in “prayer,” as Rabbi Lichtenstein and others teach, one is aware that the human mind doesn’t bring the results; it’s done by the Divine Mind accessed through the human mind. As a result, in such prayer, one not only experiences the positive results but the Divine Presence as well. The outward forms of this prayer and auto-suggestion might seem similar but the inner, cognitive process is utterly different:
“Every prayer is a suggestion but not every suggestion is a prayer.” 
This is true even of the study of Kabbalah itself. There are great Kabbalists — the Ari, Rabbi Chaim Vital, Rabbi Mosheh Cordovero, etc. — and then there are great (academic) scholars of Kabbalah — Gershom Scholem, Mosheh Idel, etc. Scholem, for example, was the first to examine the historical development of Kabbalah but would hardly be called a “kabbalist.” Scholars’ work is valuable for us, but they don’t present themselves as spiritually advanced from it. Kabbalists, on the other hand, tell us in one way or another that their study and practice have produced a change in their consciousness. Yet — both were studying the same books!
The story of an early meeting between the Baal Shem Tov and the Maggid of Mezeritch, who would become his disciple and later succeed him as leader of the Hasidic movement, similarly illustrates the point:
“…The Baal Shem Tov received [the Maggid] in his room. ‘Are you versed in Kabbalah?’ he asked. The Maggid said he was. ‘Take this book [some say R. Chaim Vital’s Tree of Life] and read.’ The Maggid read. ‘Now, think!’ He thought. ‘Explain!’ He explained the passage which dealt with the nature of angels. ‘You have no true knowledge,’ said the Baal Shem Tov. ‘Get up!’ The Maggid rose. The Baal Shem Tov stood in front of him and recited the passage. Then, before the eyes of Rabbi Dov Baer [the Maggid], the room went up in flame, and through the blaze he heard the surging of angels until his senses forsook him. When he awoke, the room was as it had been when he entered it. The Baal Shem Tov stood opposite him and said, ‘You explained correctly, but you have no true knowledge because there is no soul in what you know’…” 
Rabbi Natan’s comment (in my introduction) suggests that the early generations of Talmud-teachers saw learning Torah as a path to spiritual enlightenment.
I would say, then, that Rabbi Natan is teaching:
If one learns Torah intending to develop an intellectual understanding, one will have it — or something that resembles it — but without God.
If one learns Torah with the intention of being closer to God, of having God become a clearer Presence in one’s life, that is what one will ultimately experience.
 Tehillim/Ps. 19:9
 Saldarini S.J., A.J., trans.; The Fathers According to Rabbi Nathan (version B); Brill Publishing, © 1975; p. 184-5
 (adapted from) Friedlander, G., trans.; Pirke de Rabbi Eliezer; Sepher-Hermon Press; © 1916 , p. 7
 D’varim/Deut. 23:20
 Kohelet/Eccles. 8:1
 http://www.chabad.org/library/article_cdo/aid/2868334/jewish/Rabbi-Yehudah-bar-Ilais-Glowing-Face.htm_c; based on Nedarim 49b
 Lichtenstein, Rabbi Morris; Jewish Science and Health; © 1925 by Rabbi Morris Lichtenstein; p.75
 Buber, Martin; Tales of the Hasidim (Early Masters); Schocken Books, Inc. © 1975; p. 100 (based on “Shivchei Ha-Besht.” See:
Ben-Amos, Dan and Jerome R. Mintz; In Praise of the Baal Shem Tov (Shivhei ha-Besht); Schocken Books, © 1970; p. 81-83. This original version is longer and in greater detail than Buber’s.)