No. At least, there are not significant, accurate, or enough sources that identify seafaring by ethnographers.

The Aztec Triple Alliance was not geographically located near nor primarily inhabited at the coasts of Mexico. At least, with a large population such as Tenochtitlan to develop and consider seafaring. The Aztec Triple Alliance, forming in 1428, reached the coasts of the Gulf of Mexico during the reign of Moctezuma I (1440-1469 CE) and the later tlahtohqueh, or rulers, that expanded as far as northeast near Tuxpan, Veracruz—neighboring Otomi territories. Likewise, the Aztecs expanded to the west coast—as far as present day Cihuatlan, Jalisco—during the reign of Ahuitzotl (1486-1502 CE) and more during the reign of Moctezuma II (1502-1520 CE)—as far south as Tehuantepec, Oaxaca, with a couple of states and kingdoms neighboring.

Given this information of their expansion and the cities nearest to the coasts, the Aztecs simply did not develop the technology to set expeditions and seafaring due to cities in the outskirts of the Aztec's territories being more sparse than densely populated and those spots just joining the alliance recently. Thus, giving the rulers less time to plan what to do there extensively and instead focusing on assimilating their newly acquired lands into their alliance.

However, they were well aware of large bodies of water surrounding Mexico. Given this map, there were names for the bodies of water. Such as ayollohco for a gulf, and ilhuica(a)tl or teoatl for an ocean in classical nahuatl. Alternatively, the name of their known land was Cemanahuac, meaning "entirely surrounded by water" or "all of which is surrounded by water"; rarely meaning the "world" at times as well.

Toponymy—and in this case, hydronyms—may be relevant as they would indicate that the Aztecs were aware of bodies of water they'd consider exploring. But, they did not. As far as it goes, the Aztecs developed and sustained in a mild highland environment. Therefore, the Aztecs did not have advanced cities to take time to develop fleets and seafaring. But, there are not enough sources that show if, for example, the Atlantic ocean had a name by the Aztecs. Given this statement from this study, which explains why it may be difficult to ensure if:

La correlación de estos signos en los monumentos esculpidos y en los manuscritos precolombinos y coloniales con los topónimos documentados en lenguas mesoamericanas se ve dificultada por varios problemas de distinta índole: las discrepancias semánticas entre topónimos de los mismos lugares en distintas lenguas; el carácter tonal de algunos idiomas autóctonos (no representado en fuentes coloniales); el papel del 'rebus' en la representación fónico-pictórica de los jeroglifos toponímicos; distorsiones múltiples e interpretaciones equivocadas entre las lenguas; el préstamo de topónimos a otra lengua con sus adaptaciones fónicas y nuevas etimologías populares; las discrepancias entre nombre y signo y, además, la variación y substitución jeroglíficas.

[Translation] The correlation of these signs in sculpted monuments and in pre-Columbian and colonial manuscripts with place names documented in Mesoamerican languages is hampered by several different problems: Semantic discrepancies between place names in different languages; the tonal character of some indigenous languages (not represented in colonial sources); the role of 'rebus' in the pictorial-phonic representation of toponyic hieroglyphs; multiple distortions and misinterpretations between languages; the loan of place names to another language with its phonic adaptations and new popular etymologies; the discrepancies between name and sign; and, in addition, hieroglyphic variation and substitution.

Similarly, given Tenochtitlan being built on artificial land in a natural lake of Texcoco, the Aztecs did develop some technologies for navigation throughout the lake. The Aztecs developed several types of canoes, paddles, harbors, docks, and quays for transportation, chinampas, and trade. Just as this page about 'The Aztecs and Lake Navigation' by Mexicolore states:

The Mexica soon shaped the environment to suit their needs and to consolidate their power. The major hydraulic works that they and their neighbours on the lakes of the Valley of Mexico engineered fulfilled different objectives. The first and best documented of these, was clearly to reclaim land from the water using the ingenious system of ‘chinampas’ and canals, artificial physical extensions of pre-existing islands.

Just as you mention the Incas in the Andes, they simply had an interest and convenience of exploring the Pacific as it was adjacent to them. Similarly, the Mayans had cities and urban areas near the Yucatan coasts, such as Tulum. Hence, why the Mayans also had an interest and convenience of investing time to explore and trade in the seas, having territories primarily in the Yucatan Peninsula—an area surrounded by water.

In conclusion, no, the Aztecs didn't get to develop too much into the fields of seafaring and maritime explorations due to their geography and according to existing sources stating so.

/u/retarredroof, /u/RioAbajo and /u/Mictlantecuhtli have previously answered Before European contact, how far did trade routes extend along the Pacific coast?