No. Signing a security instrument is a property matter governed by how title and the loan are documented. Derivative status for a spouse or an unmarried child under twenty-one flows from the relationship to you as principal, plus admissibility, and follows the instructions that apply to your case.
Property signatures and derivative status are separate questions
Two practical consequences. Your spouse's signature on the pledge does not create an independent immigration filing for them, and it does not require them to already hold United States status. Separately, if your spouse's own funds contributed to the down payment, that money needs its own lawful source record.
Obtain independent advice about the property commitment and immigration advice about the funding evidence. Write down which decisions belong to the property file and which belong to the immigration file, then keep them from bleeding into one another. Hypothetical example: an investor's spouse works as a research compliance officer at an academic medical centre and assumes that signing the pledge commits them to the immigration process, when what it commits them to is a debt.
Ask your own adviser what personal liability the signature creates and over what period, and ask the immigration adviser separately what evidence the funding arrangement now requires. Derivative status for a spouse or an unmarried child under twenty-one follows the relationship to the principal and admissibility, and no signature on a security instrument advances it or replaces it.