Should I read the whole Quran before becoming Muslim?

What's actually required

To become Muslim, you sincerely testify that there is no god but Allah and that Muhammad ﷺ is His messenger. Part of that belief is accepting the Quran as God's word, but accepting it doesn't mean you've already read every page. You can't be expected to know a book of 114 chapters before you even begin. See How do I take my shahada?

The first Muslims heard only a little

The Quran was revealed over 23 years, so the earliest Muslims accepted Islam when only a few chapters existed. Later, people often converted after hearing one passage. Jubayr ibn Mut'im said that hearing the Prophet ﷺ recite Surah at-Tur in prayer was the moment faith first settled in his heart (Sahih al-Bukhari 4023). A short passage that speaks to you can be enough.

Why reading some of it is still wise

It helps to know what you're committing to. Reading even part of the Quran shows you how it describes God, the prophets, the afterlife and how to live. Allah describes it as accessible to anyone who sincerely wants to understand:

Good places to start: Surah al-Fatihah (1), the last short surahs (like 112, 113, 114), Surah Maryam (19) and Surah Yusuf (12). See Where should I start reading the Quran as a new Muslim?

Reading it all is a lifelong project

Many born Muslims first read the whole Quran with understanding as adults. Reading it cover to cover in translation takes most people several weeks or months at a comfortable pace. See How long does it take to read the whole Quran? If you wait until you've finished before making a decision you already feel sure about, you may delay for no reason. You can keep reading as a Muslim, with more support and context.