It is explicitly clear from the language of the Rambam and the Tur that we do not maintain her status as a doubtful kiddushin, but rather as certain kiddushin. The practical legal difference is that if she received kiddushin from another, the kiddushin do not take effect (Bach and Beit Shmuel, subsection 3). It is a simple matter that this applies specifically when the witnesses saw them and they saw the witnesses, as was written in the previous siman, section 10, in the name of the Tur. Our teacher, the Rema, wrote, and this is his wording: "Or if it is revealed to all that he had relations with her, such as if he married her." Thus far his words. Meaning, that this also has the status as if he had relations with her before witnesses. The Tosafot wrote a similar reasoning in Yevamot (45b, s.v. Mi) regarding immersion; see there. We have already mentioned this in siman 26, section 5; see there. There is further proof for this reasoning from what our sages, of blessed memory, said (ibid. 109b) regarding a minor who did not perform mi'un and grew up and stood and married, that she does not require a get from the second [husband] because the first had relations with her afterward certainly for the sake of kiddushin, as he knows that the kiddushin of an orphaned minor are nothing. And even the one who disagrees there, his reason is that he had relations based on the initial kiddushin; see there. But in the case of a divorcee, this does not apply. And there, there are no witnesses to the act of relations, but rather since she dwelt under him in the manner of a husband and wife, his having relations is like witnesses. So too here, since our sages, of blessed memory, said that if he had relations before witnesses he certainly had relations for the sake of kiddushin, if so, even when it is revealed to all that he married her—meaning they lived together in the manner of husband and wife—it is no less than witnesses. However, one could reject this, as there it deals with a case where it is known to us that he had relations with her, according to the plain meaning of the language of the Gemara there. However, the Rivash wrote at the end of siman 193, and this is his wording: "And the Ra'ah, of blessed memory, wrote that a minor who grew up does not even require witnesses of seclusion, for since she is his wife and remains with him, everyone knows that he secluded himself with her and had relations with her." Thus far his words. However, the Rivash himself at the end of siman 6 brought this in the name of the Ra'ah and wrote that this is a minority opinion, for all the Rishonim wrote that she requires witnesses of seclusion; thus far his words (and see Mishneh LaMelekh, chapter 11 of Hilkhot Gerushin, halakha 6). And it appears to me that in siman 6 he only wrote this regarding his question there, where she had never been his wife according to the religion of Israel; see there. Nevertheless, there are those who hesitate regarding this ruling (Beit Shmuel, subsection 1), and therefore one should follow the stringent view regarding the prohibition of a married woman.
ומבואר להדיא מלשון הרמב"ם והטור שלאו בקדושי ספק מחזקינן לה אלא בקדושי וודאי ונ"מ דאם קבלה קדושין מאחר אין הקדושין תופסין (ב"ח וב"ש סק"ג) ודבר פשוט היא דדווקא כשהעדים ראו אותם והם ראו את העדים כמ"ש בסי' הקודם סעיף י' בשם הטור ורבינו הרמ"א כתב וז"ל או שגלוי לכל שבא עליה כגון שנשאה עכ"ל כלומר דגם זה דינו כאלו בעלה בעדים וסברא כזו כתבו התוס' ביבמות (מ"ה: ד"ה מי) לעניין טבילה ע"ש וכבר הזכרנו זה בסי' כ"ו סעיף ה' ע"ש עוד יש ראיה לסברא זו ממה שאמרו חז"ל (שם ק"ט:) בקטנה שלא מיאנה והגדילה ועמדה ונשאת שאינה צריכה גט משני מפני שהראשון בעלה אח"כ וודאי לשם קדושין שיודע שאין קדושי קטנה יתומה כלום ואפילו מאן דפליג שם טעמיה דעל דעת קדושין הראשונים בעל ע"ש אבל בנתגרשה לא שייך זה והתם ליכא עדים על הביאה אלא כיון שישבה תחתיו כדרך איש ואשתו ובעלה הוה כעדים וה"נ כיון שאמרו חז"ל דאם בעלה לפני עדים וודאי בעל לשם קדושין וא"כ גם כשגלוי לכל שנשאה והיינו שדרו יחד כדרך איש ואשתו לא גרע מעדים אך שיש לדחות דשם מיירי שידוע לנו שבעלה כפשטא דלישנא דגמ' שם אך הריב"ש כתב בס"ס קצ"ג וז"ל והרא"ה ז"ל כתב דקטנה שהגדילה אפילו לעידי יחוד א"צ דכיון דאשתו היא ועומדת עמו כ"ע ידעי שנתייחד עמה ובא עליה עכ"ל אמנם הריב"ש בעצמו בס"ס ו' הביא זה בשם הרא"ה וכתב שזה דעת יחיד שכל הראשונים כתבו שצריכה לעידי יחוד עכ"ל (ועמל"מ פי"א מגירושין הל' ו') ויראה לי שבסי' ו' לא כתב זה רק לעניין שאלתו שבשם שלא היתה מעולם אשתו בדת ישראל ע"ש ומ"מ יש מפקפקים על דין זה (ב"ש סק"א) ולכן יש לילך לחומרא באיסור א"א: