Yes, it forbids marrying more than four, but not from Qur'an alone can one derive this ruling; neither the tafsir, nor the reasons for revelation in isolation. This is especially the case when based on a single verse that could mean multiple things (Arabic: ظنى الدلاله). Rulings are typically derived from multiple sources, Islamic and linguistic, by scholars who specialize in the fundamentals of jurisprudence (Arabic: علم الأصول, 'Ilm am-Usūl).
The general meaning of the words are used to derive a ruling, not the specificity of the reasons (see below for explanation). What you are asking about:
I'm wondering what would happen if the first condition were false, i.e., the man does not fear that he "will not deal justly with the orphan girls".
is a reason for revelation, but the ruling applies whether the condition exists or not.
The ruling in question derived from An-Nisa' 4: is corroborated by the hadiths that explain it and that narrate that those who had more than four wives were asked to keep only four. For example:
- When 'A'isha was asked about this verse, she explained the background in Sahih Muslim 3018 a: the orphan girl is one who is under the patronage of her guardian and she shares with him in his property and her property and beauty fascinate him and her guardian makes up his mind to marry her without giving her due share of the wedding money and is not prepared (to pay so much amount) which anyone else is prepared to pay and so Allah has forbidden to marry these girls but in case when equity is observed as regards the wedding money and they are prepared to pay them the full amount of the wedding money and Allah commanded to marry other women besides them according to the liking of their heart.
- As in Sunan Abi Dawud, Hadith 2241, when Whab al-Asadi embraced Islam with eight wives, the Prophet ﷺ ordered him to keep only four.
- In Muwatta Malik, Book 29, Hadith 1238, when a man from Thaqif who had ten wives became a Muslim, the Prophet ﷺ ordered him to keep only four.
There are other references similar to the ones above that resulted in the ruling of four being accepted as the maximum for Muslim men, except for the Prophet ﷺ, who was instructed to keep his wives while adding some restrictions on whom he could marry, and a condition for his wives that they would be eligible for re-marriage after his death.
See below for other examples of verses that have rulings based on reasons but are widely applied.
The final point is on the purpose mentioning the reason in this verse serves. It is to be able to identify linguistically what type of commandment that is.
When asking for forgiveness, one uses a command form (Forgive me, my Lord or ربى اغفر لى). While almost everyone would agree that this is a request to Allah that He may or may not grant, the form is, nonetheless, that of a command. The ability to discern that this is a request is that it comes from an inferior (humans) to their superior (Allah).
Similarly, in this verse, the command to marry (Arabic: فَانكِحُواْ) two, three, and four may seem that it is obligatory for men to marry four wives. The addition of the words "those that please you" (Arabic: مَا طَابَ لَكُم) linguistically indicates that it is mandūb (preferred) to do so. The addition of a condition if one fears that one will not be just then one marries only a single wife (Arabic: فَإِنْ خِفْتُمْ أَلَّا تَعْدِلُوا فَوَاحِدَةً) takes it to the level of being permissible.
Based on all of the above, the rule is that it is permitted for a man to marry up to four wives.
Rulings are not typically derived based on a single verse, except if that verse is a clear stipulation of an evidence (Arabic: قطعى الدلاله).
General meaning of the words are used to derive a ruling, not the specific reason(s)
The rule in fundamentals of jurisprudence is that the general meaning of the words are used to derive a ruling, not the specific reason(s) for revelation (Arabic: العبرة بعموم اللفظ لا بخصوص السبب). See Meaning of the verse "and do not throw yourselves into destruction" for an example).
In the case of An-Nisa' 4:3, the specific reasons for revelation are explained below in a hadith by 'A'isha, but the general words of the rulings prevail.
The rule that the general meaning of the words are used to derive a ruling, not the specific reason(s) for revelation is generally accepted by the majority of established scholars, with the known exception of al-Muzani and Abu Thawr, followers of the Shafi'i school of jurisprudence.
Having said that, when the condition is explicitly stipulated as being the only reason (Arabic: سبب بدليل تخصيص), it cannot be made general (Arabic: قطعية خصوص السبب). The rule has conditions:
- There has to be a distinction of what is generalizes a rule based on a specific reason (as is the case of the verse in question), versus what is can be a common attribute that falsely leads one to generalize it and derive a fallacious rule (e.g., a cat has four legs; a dog has four legs [the common attribute]; therefore, a dog is a cat [fallacy]).
- There has to be no other verse (Qur'an or hadith) that specifies conditions for a specific situation to be generalized if there is another verse that elaborates, or adds a restriction, or puts a condition, or ... For example, in this hadith, the Prophet ﷺ lists three reasons for executing a person in Islam (specific conditions) that were elaborated upon in later or other hadiths for people who commit other sins punishable by death (e.g., rebelling against a rightful ruler, committing homosexual acts, etc.). One cannot, therefore, derive a rule that other acts are not punishable by death because the specificity of the reasons for punishment are clear, the reasons for generalizing this case to be exclusive is not supported by other verses.
Examples of verses that have rulings based on specific reasons of revelation but are widely applied
In An-Nisa' 4:58, Allah Allah commands us to render trusts to whom they are due and when we judge between people to judge with justice. The reason the verse was revealed is the story related to Uthman ibn Talha, which is briefly mentioned in the link under "Conquest of Mecca". This is a type of verse that stipulates the commandment, but not the reason of revelation.
Another example is in Al-Ma'idah 5:32 where Allah narrates the story of the sons of Adam, where one kills another to marry his sister, then Allah tells us that it was prescribed upon Bani Isra'īl a specific extrapolation of the act on Judgment Day (whoever kills a soul unless for a soul or for corruption, it is as if he had slain mankind entirely). Note that the verse mentions the specific reasons, and a relevant extrapolation for accountability in front of Allah, but the earthly ruling of punishment remains to be the execution of the murderer.