Short answer. No. Article 1491 of the Civil Code lists the guardian among the persons who cannot acquire by purchase the property of the person or persons who may be under his guardianship. The guardian's duty to protect the ward's property bars him from buying it for himself.
What the law says
The guardian, the property of the person or persons who may be under his guardianship
Civil Code, Article 1491 — Persons Who Cannot Buy. Read the full provision →
The guardian sits at the top of the list
The law names the guardian first among those who cannot buy property they are meant to look after. The relevant clause bars, from acquiring by purchase, the guardian, the property of the person or persons who may be under his guardianship. The prohibition is specific to that relationship: it concerns the ward's property, which the guardian is entrusted to manage and protect. A guardian is free to buy property in the open market like anyone else; what he cannot do is turn his position over the ward's assets into an opportunity to acquire those very assets for his own account.
Why the law forbids it
The reason is the plain conflict of interest. A guardian is supposed to secure the best terms for the ward, which on a sale means the highest price and the most favorable conditions. If the guardian is also the buyer, his private interest is to pay as little as possible, directly opposed to the ward's interest he is bound to serve. Wards are often minors or persons who cannot fully protect themselves, so the law does not rely on the guardian's good faith case by case; it removes the temptation altogether by prohibiting the purchase outright.
The ban cannot be dodged by indirect means
The article closes the obvious escape routes. It applies whether the guardian buys in person or through the mediation of another, so putting a relative, friend, or nominee forward as the ostensible buyer does not save the transaction if the guardian is the real acquirer behind it. It applies even at a public or judicial auction as well, meaning the guardian cannot rely on the property being sold through an open or court-supervised process. The prohibition follows the substance of who is really acquiring the ward's property, not merely the name on the paperwork.
What a guardian should do instead
A guardian who genuinely believes a sale of the ward's property is in the ward's interest should carry it out for the ward's benefit and to a buyer who is not himself, keeping the process transparent and, where required, within the supervision the law provides for a ward's affairs. If the guardian has a real personal interest in acquiring the property, the clean course is to step aside from that transaction entirely. Attempting to buy the ward's property, directly or through a stand-in, exposes the sale to being undone and casts doubt on the guardian's stewardship as a whole.