Short answer. Yes. Article 1825 provides that when all the members of the existing partnership consent to the representation, a partnership act or obligation results — a genuine partnership debt, not merely that individual's personal liability. Only where consent is not unanimous does the obligation remain the joint obligation of the specific consenting persons.
What the law says
When all the members of the existing partnership consent to the representation, a partnership act or obligation results; but in all other cases it is the joint act or obligation of the person acting and the persons consenting to the representation.
Civil Code, Article 1825 — Partnership by Estoppel. Read the full provision →
The unanimous-consent rule
Article 1825 closes with a rule that answers your question directly. It states that when all the members of the existing partnership consent to the representation, a partnership act or obligation results; but in all other cases it is the joint act or obligation of the person acting and the persons consenting to the representation. Since you describe all the actual partners as having known about and agreed to the false representation, this is exactly the scenario the first branch of that sentence covers.
Why unanimity matters here
Unanimity is the dividing line the article draws. Where every member of the real, existing partnership consented to someone being represented as a partner, the resulting obligation is treated as an actual partnership obligation — not a personal debt belonging only to the person who made the misrepresentation, and not a limited obligation shared only among some of the partners. Full consent from the whole partnership produces a full partnership-level consequence.
What happens without unanimous consent
Where consent is not unanimous — meaning only some of the partners knew of and agreed to the representation, or none did — the article treats the resulting obligation differently. It becomes, in the article's words, the joint act or obligation of the person acting and the persons consenting to the representation. That obligation is confined to the specific individuals who acted or consented, rather than binding the entire actual partnership or every one of its genuine members.
How this fits with the pro rata and whole-liability rules
This unanimous-consent rule works alongside the article's earlier distinction between full partnership-style liability and pro rata or separate liability. Where all the partners consented, as in your situation, the debt is a genuine partnership obligation, which generally carries the same consequences as any other partnership debt — a different and more far-reaching result than the pro rata liability that applies when the misrepresentation was consented to by only some of the people involved, or by none of the actual partners at all.