The Rambam apparently believes that the tinoq shenishba is defined by the attitude he/she was raised with toward Torah, not only their ignorance of it. And so even after learning Torah, as long as his motivation was at least founded on the initial bias against believing its truth or applicability, the tinoq shenishba is not held to account.
To quote the Rambam's Code, Hilkhos Mamrim 3:1-3 (emphasis mine, tr. R' Zvi Lampel):
בַּמֶּה דְּבָרִים אֲמוּרִים בְּאִישׁ שֶׁכָּפַר בַּתּוֹרָה שֶׁבְּעַל פֶּה בְּמַחֲשַׁבְתּוֹ וּבִדְבָרִים שֶׁנִּרְאוּ לוֹ. וְהָלַךְ אַחַר דַּעְתּוֹ הַקַּלָּה וְאַחַר שְׁרִירוּת לִבּוֹ וְכוֹפֵר בַּתּוֹרָה שֶׁבְּעַל פֶּה תְּחִלָּה כְּצָדוֹק וּבַיְתּוֹס וְכֵן כָּל הַתּוֹעִים אַחֲרָיו. אֲבָל בְּנֵי הַתּוֹעִים הָאֵלֶּה וּבְנֵי בְּנֵיהֶם שֶׁהִדִּיחוּ אוֹתָם אֲבוֹתָם וְנוֹלְדוּ בֵּין הַקָּרָאִים וְגִדְּלוּ אוֹתָם עַל דַּעְתָּם. הֲרֵי הוּא כְּתִינוֹק שֶׁנִּשְׁבָּה בֵּינֵיהֶם וְגִדְּלוּהוּ וְאֵינוֹ זָרִיז לֶאֱחֹז בְּדַרְכֵי הַמִּצְוֹת שֶׁהֲרֵי הוּא כְּאָנוּס וְאַף עַל פִּי שֶׁשָּׁמַע אַחַר כָּךְ [שֶׁהוּא יְהוּדִי וְרָאָה הַיְהוּדִים וְדָתָם הֲרֵי הוּא כְּאָנוּס שֶׁהֲרֵי גִּדְּלוּהוּ עַל טָעוּתָם] כָּךְ אֵלּוּ שֶׁאָמַרְנוּ הָאוֹחֲזִים בְּדַרְכֵי אֲבוֹתָם הַקָּרָאִים שֶׁטָּעוּ. לְפִיכָךְ רָאוּי לְהַחְזִירָן בִּתְשׁוּבָה וּלְמָשְׁכָם בְּדִבְרֵי שָׁלוֹם עַד שֶׁיַּחְזְרוּ לְאֵיתָן הַתּוֹרָה:
.... However, this is speaking solely of those who ... initiate such denial, such as Tzadoq and Boethus. But the children and grandchildren of these kinds of men, who were misled by their fathers, that is, those who were born into and bred by the Qaraites, are like people who while still young had been taken into captivity and raised in another religion. Such captives are not quick to take hold of the mitzvos, for their situation is practically beyond their control: Even if they later hear that they are Jewish and are exposed to Jews and Judaism, they still are considered people who practice another religion only by force, since they were raised and educated erroneously. The same is true with those who keep the ways of their erroneous Karaite fathers.
A tinoq shenishba is mentioned in the gemara (Shabbos 68a) as a kind of oneis (someone who sins through no fault of his own); someone who never knew is less culpable than a shogeig (someone who sins because of forgetting). And thus, "oneis Rachamana patreih -- the All-Merciful forgives the oneis". (BQ 28b, AZ 54a, Nedarim 27b) Which is only logical. Someone who forgot is culpable to the extent that they should have taken the matter more seriously, then they could have remembered. But a tinoq shenishba's attitude toward observance is a product of circumstance.
And so, a tinoq shenishba would presumably not suffer for it in the afterlife.
(In general, later sources describe one's fate in the afterlife in terms of one's progress in this world; not absolute accomplishment. While that's a broader topic, you question would fit as one example.)
I therefore don't think you have to worry about part of your question. The Rambam would say there is no "chance they have stopped having the status of Tinok shenishba bein hanachrim [nor] risk becoming an apikoros or kofer".
However, you close with, "Do they still get forgiven and admitted into Olam HaBa?"
This presumes the Rambam believes that admition into the World to Come depends on culpability. It can be argued either way. There are strong indications he sees one's place in the World to Come as having a cause-and-effect relationship to one's Knowledge.
For example, Hilkhos Teshuvah 8:1:
... וְזֶה שֶׁאָמְרוּ צַדִּיקִים יוֹשְׁבִין דֶּרֶךְ חִידָה אָמְרוּ. כְּלוֹמַר הַצַּדִּיקִים מְצוּיִין שָׁם בְּלֹא עָמָל וּבְלֹא יְגִיעָה. וְכֵן זֶה שֶׁאָמְרוּ עַטְרוֹתֵיהֶן בְּרָאשֵׁיהֶן כְּלוֹמַר דַּעַת שֶׁיָּדְעוּ שֶׁבִּגְלָלָהּ זָכוּ לְחַיֵּי הָעוֹלָם הַבָּא מְצוּיָה עִמָּהֶן וְהִיא הָעֲטָרָה שֶׁלָּהֶן...
And that which [the Sages] said that the righteous sit [in the World to Come], they spoke in a metaphoric manner. As to say, the righteous are present there without work of effort. Similarly, that which they said "their crowns on their heads", so as to say, the knowledge which they knew because of which they merited to life of the World to Come is found with them and is their "crown"...
Or your quote from the opening of his list of 13 Iqarim [Articles of Faith].
(Similarly, the Guide 3:18 describes knowledge as the key to being a "person" in the sense of getting hashgachah peratis [individual Divine Providence], prophecy is defined as the overflow of Knowledge from the Active Intellect to the prophet's intellect, the closing chapter calls Knowledge the highest human perfection, and so on.)
If he means this causally, then someone who lacks the requisite Knowledge simply lacks what it takes to get a place in the World to Come. Whether it's their fault or not.