Short answer. No. When the buyer already holds the thing for another reason, no new physical handing-over is required. Article 1499 lets delivery of movable property be made by the mere consent or agreement of the parties where the buyer already had it in his possession for any other reason. Their agreement completes the delivery.
What the law says
The delivery of movable property may likewise be made by the mere consent or agreement of the contracting parties, if the thing sold cannot be transferred to the possession of the vendee at the time of the sale, or if the latter already had it in his possession for any other reason.
Civil Code, Article 1499 — Traditio Brevi Manu / Longa Manu. Read the full provision →
Delivery by agreement, not by re-handing
Delivery normally transfers ownership in a sale, and we tend to picture it as physically passing the thing from one hand to another. Article 1499 recognises that this is sometimes unnecessary or impossible. It allows that the delivery of movable property may likewise be made by the mere consent or agreement of the contracting parties in two situations: where the thing cannot be transferred to the buyer's possession at the time of sale, and — your case — if the latter already had it in his possession for any other reason. Since the buyer is already holding the item, the law treats the parties' agreement as accomplishing the delivery, without an idle ceremony of handing it back and forth.
Why re-delivery would be pointless
The rule is common sense turned into law. If the buyer already possesses the thing — say he was holding it as a borrower, lessee or depositary — then requiring the seller to take it back only to hand it over again would achieve nothing but ritual. What changes on the sale is not who is physically holding the object but the capacity in which he holds it: he ceases to hold it for the seller and begins to hold it as owner. The parties' consent effects that shift. This is why the moment of the agreement, rather than any new transfer, is treated as the delivery.
What the change of possession does
Because delivery is what generally passes ownership in a sale, treating the agreement as the delivery means ownership can transfer even though nothing visibly moves. The buyer, already in possession, now holds the thing on his own account. This matters for practical questions that turn on ownership and possession — who bears the risk of loss going forward, and who may deal with the thing as owner — all of which flow from the completed delivery the article recognises. The seller has performed his duty to deliver simply by consenting, and cannot be asked to perform it again.
The limits of this shortcut
The article deals with how delivery may occur; it presupposes a valid sale with the buyer genuinely already in possession for some prior reason. It does not dispense with the need for a real agreement — the mere fact that a person holds a thing does not, without a sale, make him its owner. It also does not resolve competing claims to the same movable, or the position of third persons who dealt with the item, which other rules govern. And it applies to movable property; the transfer of ownership in land and other immovables follows its own requirements.