Well, I see a major ideological problem with this. The spreading of God's word and Catholic faith to those poor and infantile indians that had not had the occasion to be gifted with it was the driving auto-justificative element of the spanish imperialism as the
mission civilisatrice and white man's burden was for the french and british latter. So, helping to spread a rival faith throught the New world doesn't seem very coherent with that conception.
However, as I said in the thread about the renish moriscos, the spanish moriscos were technically catholics. If they were sent to the Americas I expect they would be under certain conditions, mainly I can think in two:
-They will remain catholics and they will be obligated to baptise their offspring.
-Geographical concentrations of moriscos would be avoided, trying to spread them as much as possible around the empire, in order to minize their ability to create local influence or troubles.
Of course, most of the moriscos continued being muslims in more or less veiled ways. So, under these conditions, they could influence the spanish-american cultuture making it even more original, but always through underground ways, never openly. Thus, I can't see a muslim majority living in a spanish colony.
Another question would revolve around their place in the colonial society, and their rights regarding properties, specially regarding the
encomiendas. Would them be treated equally to other spaniards or would them used as semi-slave workforce like in many parts of the crown of Aragon? and regarding that, Would it affect only to the castilian moriscos or would it include also the aragonese? Would them constitute a differentiated
casta?
We can also take into acount the examples from OTL. There were some moriscos, as jews, in the spanish Americas. Obviously it's a different situation because they were few and sometimes under covert identities to hide their origin. Many of them were women forced to go to the Americas due to the lack of women among the colonizers, often made slaves by "right of war" after the uprisings of the
morerías or captured in the mediterranean raidings so usual in both shores. They obviously mixed quickly with the "old christian" lineages. We have also the case of Cristobal de Burgos, an openly morisco who went to Peru with Pizarro's expedition and reached a high post in the vicerroyal administration. Another "famous" case is the so-called
Emir Cigala, I have forgot his true name, sorry. That emir Cigala, is said, went to the Americas with a false identity, get rich in Potosí and returned to Spain. Also Diego de Almagro was accused several times of being morisco, though we can't take it as a serious evidence. We don't know much about the less remarkable moriscos in the Americas, specially because they used castilian names so it's very difficult to identify them in the documentation. It seems that most of them didn't have many problems in the colony, probably because neither at the time nobody could diferenciate a morisco from a "old christian" if its not told. There is
mudejar influence in early colonial architecture, by the way. But once again I don't know at what point it can be projected to the OP's question, since in this case they would be a recognizable and marked minority and not more or less sporadic cases.
Cheers.