The question of intentional the spread of infection through "smallpox blankets" is debatable. I write a bit about the accusation of the British using smallpox against the Americans during the Revolution here, and /u/reedstilt did a great write up on the subject in /r/badhistory here. The conclusion of both comments is that we have exceedingly few instances of disease being used intentionally in warfare, and almost no evidence that these attempts were effective. Epidemics were either already raging or primed to start from other sources. My own opinion is that focusing on the exceptionally rare "smallpox blankets" is a dodge on focusing on the very real brutality and inhumanity that Euro-Americans inflicted on Native peoples who were devastated by naturally occurring and spreading epidemics.

The thing about pathogens which have routinely caused epidemics throughout human history is that they really don't need any help from people to spread. They can certainly be prevented from spreading by preventative measures, but this requires a level of knowledge that wasn't really present until the late 19th/early 20th century.

That said, the answer to you question is "no."

Thanks! That'll be $20!

Seriously though, we have no zero indication that the Spanish intentionally tried to spread smallpox in Mexico during the 1520 epidemic. We have multiple accounts that smallpox arrived in Mexio with an African servant named Francisco Eguia, who accompanied the Narvaez expedition. Narvaez had been sent to bring Cortés back to Cuba in chains. After most of the men defected to Cortés and he defeated the rest of Narvaez's troops, the smallpox expedition began to spread inland from the Gulf Coast. Cortés almost doesn't mention the outbreak -- possibly because it would highlight the fact that he attacked a legal expedition assigned to arrest him -- except to mention later that he left some sick individuals behind as he traveled from the Gulf back to Tenochtitlan. That is the very opposite of trying to use a disease as a weapon.

Another Spanish account, from Bernal Díaz del Castillo, similarly makes very little mention of the epidemic. For him, it is just something that happened. We are not talking about individuals with modern conceptions of disease, we are talking about people for whom bleeding was a standard medical practice. We can see the collusion of European and Mexican mystical ideas about disease in this passage from Díaz del Castillo which describes not only the smallpox epidemic, but subsequent outbreaks:

The Mexicans relate that, shortly before our arrival in New Spain, there appeared a figure in the heavens of a circular form, like a carriage wheel, the colours of which were a mixture of green and red. Shortly after a second, of a similar form, made its appearance, which moved towards the rising of the sun, and joined the first. Motecusuma, who at that time sat upon the throne of Mexico, assembled his priests and soothsayers, and desired them to watch, and explain to him these wonderful signs, which had never been seen before. The priests accordingly communicated with their god Huitzilopochtli, who answered, that they portended dreadful wars and horrible pestilence, and that it was necessary to sacrifice some human beings.

Shortly after these signs had been seen in the heavens we arrived in New Spain, and ten months after Narvaez came, and brought with him a negro, who was ill with the smallpox. From this person the disease spread among the inhabitants of Sempoalla, and thence, like a true pestilence, throughout the whole of New Spain.

When, subsequently, we fought the severe battles during the night[Pg 407] of sorrows, and lost 550 of our men, who were either killed in our retreat or taken prisoners, and sacrificed to the Mexican idols, the interpretations which the priests had given of the signs were considered perfectly correct. These signs were not seen by any of us, but I have related this exactly as told by the Mexicans, for it is so described in their hieroglyphic writing, which we always found correct.

The following appearance I beheld with my own eyes, which any one else might have seen if he had taken the trouble of looking up. In the year 1527 there appeared in the heavens a sign, which had the shape of a long sword, and seemed as if it stood between the province of Panuco and the town of Tezcuco, and remained unchanged in the heavens for the space of twenty days. The Mexicans and their papas declared it was a sign of some pestilence, and certainly a few days after the measles, and another eruptive disease, like leprosy, broke out, which was accompanied by a very nauseous smell, and carried off numbers of persons, though it did not prove so destructive as the smallpox.

Again, these were not men for whom the modern concept of disease applies. Andrew Wear in his Knowledge & Practice of English Medicine, 1550-1680 makes the case that it was not until the late 17th century that we begin to see a substantial break from fatalistic and Galenic models of disease into what we would call "evidence based medicine."