Short answer. Yes, but the transfer isn't automatic — Article 142 of the Family Code lets the court transfer administration of all of an incapacitated spouse's exclusive property to the other spouse once that spouse becomes the incapacitated spouse's guardian, though the court will instead appoint someone else if you are disqualified by incompetence, conflict of interest, or similar cause.
What the law says
The administration of all classes of exclusive property of either spouse may be transferred by the court to the other spouse: (1) When one spouse becomes the guardian of the other
Family Code, Article 142 — Court Transfer of Administration of Exclusive Property. Read the full provision →
What the law says
If the other spouse is not qualified by reason of incompetence, conflict of interest, or any other just cause, the court shall appoint a suitable person to be the administrator.
Family Code, Article 142 — Court Transfer of Administration of Exclusive Property. Read the full provision →
Becoming guardian opens the door to administration
Article 142 of the Family Code lists becoming the guardian of the other spouse as one of the grounds letting the court transfer administration of all classes of that spouse's exclusive property to you. This covers the incapacitated spouse's own separate property — property that belongs to them individually rather than to the community or conjugal partnership — and the transfer follows from the guardianship relationship itself, not from anything else you need to separately establish once the guardianship is in place.
The court transfers administration; it does not happen automatically
Becoming your spouse's guardian does not, by itself, hand you administration of their separate property — the article says the administration may be transferred by the court, meaning it is the court that makes the transfer. Guardianship over the person and administration over separate property are treated as related but distinct matters, each needing the court's own action even though one commonly follows the other.
The other grounds for transfer
Guardianship is only one of four grounds Article 142 recognizes. The others are: the other spouse being judicially declared an absentee, being sentenced to a penalty carrying civil interdiction, or becoming a fugitive from justice or hiding as an accused in a criminal case. All four share the same underlying idea — the owning spouse is, for one legal reason or another, unable to manage their own separate property, so administration needs to pass to someone who can.
When the transfer goes to someone else instead
The transfer to you as the other spouse is not guaranteed even where one of these grounds exists. If you are not qualified — by reason of incompetence, conflict of interest, or any other just cause — the court will instead appoint a suitable person to administer the property. This safeguard means the incapacitated spouse's property is not automatically placed in the hands of whoever happens to be their spouse and guardian if that person is not, for some reason, a fit administrator for it.