I suspect Mexicans would view it as another Pancho Villa Expedition, which was also event where neither side declared war.
Not in the metaphorical "war on poverty" sort of way.
FWIW, examples in addition to Maduro are Aguinaldo (Philippines), Noriega (Panama), Hussein (Iraq), and Aristide (Haiti).
(Technically speaking, the US didn't recognize Philippine independence so didn't consider Aguinaldo to be its president, but instead a rightful cession from the Kingdom of Spain due to the Treaty of Paris, which ended the Spanish–American War, where the US had made a formal declaration of war.)
(Also, the US says Aristide's departure was voluntary.)
rather than arming the cartels to fight against the mexican government, thr US could just... not