The Rambam writes in Hilchot Issurei Biah 13:15:
לְפִיכָךְ לֹא קִבְּלוּ בֵּית דִּין גֵּרִים כָּל יְמֵי דָּוִד וּשְׁלֹמֹה. בִּימֵי דָּוִד שֶׁמָּא מִן הַפַּחַד חָזְרוּ. וּבִימֵי שְׁלֹמֹה שֶׁמָּא בִּשְׁבִיל הַמַּלְכוּת וְהַטּוֹבָה וְהַגְּדֻלָּה שֶׁהָיוּ בָּהּ יִשְׂרָאֵל חָזְרוּ. שֶׁכָּל הַחוֹזֵר מִן הָעַכּוּ''ם בִּשְׁבִיל דָּבָר מֵהַבְלֵי הָעוֹלָם אֵינוֹ מִגֵּרֵי הַצֶּדֶק. וְאַף עַל פִּי כֵן הָיוּ גֵּרִים הַרְבֵּה מִתְגַּיְּרִים בִּימֵי דָּוִד וּשְׁלֹמֹה בִּפְנֵי הֶדְיוֹטוֹת. וְהָיוּ בֵּית דִּין הַגָּדוֹל חוֹשְׁשִׁין לָהֶם לֹא דּוֹחִין אוֹתָן אַחַר שֶׁטָּבְלוּ מִכָּל מָקוֹם וְלֹא מְקָרְבִין אוֹתָן עַד שֶׁתֵּרָאֶה אַחֲרִיתָם:
For this reason, the court did not accept converts throughout the reign of David and Solomon. In David's time, [they feared] that they sought to convert because of fear and in Solomon's time, [they feared] that they were motivated by the sovereignty, prosperity, and eminence which Israel enjoyed. [They refrained from accepting such converts, because] a gentile who seeks to convert because of the vanities of this [material] world is not a righteous convert.
Our verse, Esther 8:17, states:
וּבְכָל־מְדִינָ֨ה וּמְדִינָ֜ה וּבְכָל־עִ֣יר וָעִ֗יר מְקוֹם֙ אֲשֶׁ֨ר דְּבַר־הַמֶּ֤לֶךְ וְדָתוֹ֙ מַגִּ֔יעַ שִׂמְחָ֤ה וְשָׂשׂוֹן֙ לַיְּהוּדִ֔ים מִשְׁתֶּ֖ה וְי֣וֹם ט֑וֹב וְרַבִּ֞ים מֵֽעַמֵּ֤י הָאָ֙רֶץ֙ מִֽתְיַהֲדִ֔ים כִּֽי־נָפַ֥ל פַּֽחַד־הַיְּהוּדִ֖ים עֲלֵיהֶֽם׃
And in every province, and in every city, whithersoever the king’s commandment and his decree came, the Jews had gladness and joy, a feast and a good day. And many from among the peoples of the land became Jews; for the fear of the Jews was fallen upon them.
Thus, it seems unlikely that the מתיהדים actually converted. Although the Rambam does explain that a roundabout route of conversion was open, it was designed to weed out those who converted from external concerns-- like these people.