Short answer. No, generally not. Rule 39, Section 46 provides that when judgment is rendered against your surety, you as the principal are bound only from the time you have notice of the action and an opportunity, at the surety's request, to join in the defense. Without that notice and opportunity, the judgment does not bind you.
What the law says
When a judgment is rendered against a party who stands as surety for another, the latter is also bound from the time that he has notice of the action or proceeding, and an opportunity at the surety's request to join in the defense
Rule 39, Section 46 — When principal bound by judgment against surety. Read the full provision →
What Rule 39, Section 46 provides
Rule 39, Section 46 addresses exactly this relationship: "When a judgment is rendered against a party who stands as surety for another, the latter is also bound from the time that he has notice of the action or proceeding, and an opportunity at the surety's request to join in the defense." A judgment against the surety can extend to the principal, but the rule ties that effect to a specific starting point — notice, plus an opportunity to join the defense.
Two conditions, not just one
The rule reads as a conjunction, not an either-or: the principal is bound "from the time that he has notice of the action or proceeding, and an opportunity at the surety's request to join in the defense." Both elements have to be present for the binding effect to attach — notice alone, without a real opportunity to join the defense, is not what the rule describes, and neither is an opportunity that existed only in theory without actual notice reaching the principal.
Why the rule conditions binding on notice at all
Binding a principal to a judgment reached in a case the principal never knew about, and never had a chance to influence, would let someone's rights be decided entirely behind their back. The rule avoids that by making the binding effect start only once the principal actually has notice and a real chance to join the defense at the surety's request. Fairness, not the mere existence of a surety relationship, is what the rule is built around.
What this means for your situation
If you genuinely never received notice of the action against your surety, and never had an opportunity, at the surety's request, to join in the defense, then the condition Rule 39, Section 46 sets for binding you has not been satisfied. Based on what the rule requires, a judgment reached that way would not, by this provision alone, extend to bind you as the principal.