No. Kuwait's Personal Status Law explicitly prohibits a Muslim woman from marrying a non-Muslim man. Under Article 18, such a marriage contract is considered void (not merely voidable) — it simply cannot be formed under Kuwaiti law, regardless of the couple's personal wishes or agreements made elsewhere.
This rule applies to all women classified as Muslim under Kuwaiti law, including expat women who are Muslim. If a Muslim woman attempts to marry a non-Muslim man in Kuwait, the marriage will not be legally recognised and will carry no legal rights or protections — including rights related to inheritance, divorce, or child custody.
The same article also prohibits a Muslim man from marrying a non-Muslim woman who is not a "woman of the Book" (i.e., not Christian or Jewish). Marriages involving a person who has apostatised from Islam are also void under Article 18, even if the other party is non-Muslim. If you are in an interfaith relationship and are unsure how these rules apply to your situation, consulting a Kuwaiti family law attorney is strongly advised before making any legal commitments.
This is general legal information, not legal advice. For advice on your specific situation, consult a lawyer licensed in Kuwait.