Short answer. Not quietly, and not without the principal's informed consent. The Civil Code makes an agent liable in damages where his interests conflict with the principal's and he prefers his own — and an agent who is both seller's representative and buyer is on both sides of that conflict at once.
What the law says
The agent shall be liable for damages if, there being a conflict between his interests and those of the principal, he should prefer his own.
Civil Code, Article 1889 — Preferring the Agent's Own Interest. Read the full provision →
The conflict is structural, not a question of motive
Article 1889 provides that the agent shall be liable for damages if, there being a conflict between his interests and those of the principal, he should prefer his own. An agent engaged to sell owes the principal the highest price obtainable. As a buyer, the same person wants the lowest. There is no version of that arrangement in which the two duties can both be discharged, which is why the objection does not depend on proving the agent was dishonest. The problem is the position he put himself in, and the natural pull it exerts on every judgment he makes about price, offers and timing.
Consent is what changes the analysis
The article penalises preferring one's own interest, not merely having one. Where the principal is told plainly that the agent wishes to buy, on what terms, and what the agent knows about the property's value, and the principal agrees with that knowledge, the agent is no longer choosing between two masters — the principal has chosen for him. The disclosure has to be real to have that effect. A buried clause, a mention after the fact, or a half-account that leaves out an offer the agent had already received is not consent to anything, and leaves the conflict exactly where it was.
Buying through someone else does not solve it
The most common version of this is not the agent signing as buyer. It is a purchase through a relative, an employee, or a company the agent controls, followed shortly by a resale at a higher figure. The conflict is the same conflict, whatever name appears on the deed, and the resale is often what exposes it. The other pattern worth naming is the agent who takes something from the buyer's side as well — a fee, a commission, a share of the resale — while collecting from the principal. Compensation from the other side of a deal is the plainest form of preferring one's own interest there is.
What to check, and what damages actually means here
Article 1889 speaks of liability for damages. It does not, by itself, undo the transfer, and unwinding a completed sale is a separate and harder question that depends on the terms and on who else has since acquired an interest. So gather the material that shows what the property was really worth and what the agent knew: offers received, the valuation, the marketing record, the dates, and the chain of ownership after the sale. Take that to a lawyer promptly. What can be recovered, and whether the sale itself can be attacked, narrows as time passes and as third parties come in.