To answer this questions any lawyer would need more information about the circumstances of the tort and what you mean by foreign. It is also not clear which court you are referring to. Technically, however, there is no blanket prohibition against a state or federal court (federal courts are located within states and also apply state law) and gaining jurisdiction over a general partnership, even a foreign one, regardless of the statutory agent issue. There are many technical issues that would affect service of process and the application of various jurisdictional tests. More information would be needed about your particular situation.
The only way to know for sure is to sue or be sued and see if the court grants or denies a motion for lack of jurisdiction. There is not simple answers to this situation.
Please note that I am answering this question as a service through Avvo but not as your attorney and no attorney-client relationship is established by this posting. An attorney-client relationship can only be established through signing a Fee Agreement and paying the necessary advanced fees.
If the tort occurred in Arizona, and the tort was done on behalf of the partnership, then most likely Arizona courts are going to have jurisdiction over the partnership. Depending on the type of tort, there might be a fight over whether it "occurred" in Arizona, and there might also be a fight over whether the tort was "done on behalf of the partnership." But that's the general rule that the court will apply in deciding whether it has jurisdiction.
This answer does not constitute legal advice. I am admitted in the State of Arizona only. This advice is based on general principles of law that may or may not relate to your specific situation. Facts and laws change and these possible changes will affect the advice provided here. You should not rely on this advice alone, and nothing in these communications creates an attorney-client relationship.