Yes, But Venetian Army was mostly mercenary (not as the Spanish-Portuguese, English) and I don´t know about Venetian standing Embassy in Madrid or in London from 15th Century. iN any case, Venetian State was very important in Europe in Medieval Age. When the Spaniards (Colón) and Portuguese (Vasco da Gama) arrived to America and India... Venetia was fatally wounded.
The first stable embassy were established in the Italian states around half of XV century (Mantova or Venice were the first). Also the Bailo of Costantinople from XIII century was an ambassador.
The fatal wound to Venetian wasn't inflicted by Colombo, but by the Ottoman that compromised the commerce with the Levant.