Almost certainly not, no - at least not in the way that you imagine.

The most immediate barrier to the development of a West African literary tradition in the New World would be the lack of materials to write with in a sustainable way and the difficulty of transmitting written messages across a community. It's important to keep in mind that as fully literate people, we are somewhat exceptional in the history of humanity to date - probably around one eighth of white people were still illiterate by 1860 in the United States, and we know that a far higher number of people would be considered functionally illiterate (able to comprehend basic writing, but not able to read with such ease that they could reliably do a job that depends on reading for information, or read independently for personal development). The materials for writing would have been very difficult to come by for enslaved people in large communities, and whilst fragmented communication or recording of information may have been possible, the conditions would never have existed under slavery for the sustained development of writing or the transmission of information. Nothing resembling the kind of culture of writing that existed in contemporary white society would have been possible.

Much more significantly though, West African language in this period was exclusively or heavily oral. The vast majority of African languages today make use of Latin or Latin-derived scripts for this reason. The norm in West African cultures of the age was an elaborate and sophisticated system of transmitting information orally. To our modern western ears this sounds like a very unreliable and difficult thing to do but this is just the result of growing up in a culture where written language reigns supreme and literacy is the norm, and a surprising amount of our own now-written cultural lore in Europe has its origins in long forgotten oral traditions - and much popular history has an oral component to it (think of documentaries that interview people of note, their descendants and their biographers to help flesh out the story of the past). Societies that depend upon oral tradition and the oral transmission of information develop very effective rules, traditions, procedures and norms for policing authority, quality and accuracy. Asking a respected carrier of an oral tradition in West Africa would not be the same thing as asking your grandparents what they did in the war. Whilst the absence of written records is problematic for the methods employed by most historians, there is no inherent reason why a written account of an event is necessarily any more reliable than an oral one. Flaws of human perspective, memory, bias and selectivity apply to both the written and spoken word - albeit in slightly different ways.

These oral traditions were very much carried across into the Americas by enslaved Africans and transmitted to their descendants, particularly in the early period of slavery. Alex Haley's Roots has several powerful fictional examples of this, the most memorable being how the titular character Kunta Kinte recreates the naming ritual he experienced as a baby for his daughter Kizzy when she is born. Haley's decision to write the book was inspired by his own family passing down stories and pieces of information about the life of Kinte and his other ancestors. The oral nature of these traditions and the utter disinterest or outright hostility on the part of white observers to their existence makes tracking them difficult, but the evidence for them litters slavery. The social structure of enslaved communities has clear roots in many traditional West African structures adapted to the extremely difficult conditions in which those communities formed. Even where and when Christianisation ostensibly took place (and converting African people or their descendants to Christianity was never a major theme of transatlantic slavery), religious practice and imagery is filled with distinctly African symbolism. Many enslaved communities developed means of communicating important information and news to each other; men and women who worked in close proximity to white people on a day to day basis would find a reason to be nearby when they discussed the contents of the day's mail or newspaper, and pass this information verbally back to their friends, families and communities. White racial prejudice often left slave owners oblivious to the fact that the forced labour they employed in their domestic lives might well be taking advantage of their proximity to them.

West Africa did have some pictographic systems that resemble writing that may have been reproduced in the New World. For example in the Ashanti region of Ghana there is an historic system of visual symbols called Adinkra. Though numerous and elaborate, these symbols do not qualify as a written language - they are not a written representation of Twi, the language spoken by the Akan people of the Ashanti region (who often get mistakenly referred to just as "the Ashanti" when talking about slavery, confusing the Akan people with the historic Asante state, created by one particular community of the Akan people), and you can learn the meaning of Adinkra without learning Twi. Each symbol instead has an abstract meaning to the Akan - it might represent a cultural concept, something in the environment, a famous proverb, a notable character in Asante history and so on. Whilst sophisticated and elaborate, in terms of their functionality these symbols are more comparable to abstract road signs (although that doesn't remotely capture their cultural significance) than written English - you can only understand them if you understand the particular context they exist in.

It is possible that symbol systems like this were used by enslaved people as a means of communicating away from the white gaze and to assert an African identity. This would have been complicated however by the fact that the people Europeans took from Africa were from extremely diverse communities - sometimes separated by hundreds of miles. A single slave ship might carry men, women and children from dozens of different cultures or localities, including some who had come from further East or South than you would normally expect. We have to date identified an astounding 464 possible distinct linguistic origins for the 90,000 or so native African names we have for victims of the slave trade. This was not an accident of the trade - dividing people by language and culture was a powerful tool to demonstrate both the power of white slavers and to diminish the risk of revolt or resistance on slave ships by making the coordination of any kind of activity extremely difficult. Whilst enslaved people may have been able to find commonalities in physical symbolism to construct a new iconography, it would have been impossible to develop any kind of sustained new iconography that could be recognised by most arrivals to the Americas, as any new system would be the product of particular interactions within a single community. And again, these systems are not true written language. In the same way that knowing the equal-armed cross sign outside of a building indicates a medical establishment does not mean you can speak French just because you can use it to find a pharmacy or clinic in France, knowing the cultural meaning of an Adinkra symbol does not bring you any closer to speaking Twi.

There is one supposed exception to all of this that I am aware of. In the 1910s/1920s a man by the name of Dr. Thomas Narven Lewis created a script for the Bassa language - spoken chiefly in Liberia - which has no known historic written form, barring another abortive attempt to create a written script in the 19th century. It is claimed by some advocates of the script's use over Latin that Lewis's alphabet was reconstructed from symbols he had been taught by the descendants of slaves in the Americas, who in turn claim they originate with an ancestor who was a Bassa speaker. Unfortunately depending on who you ask, that teaching happened alternately in Brazil, the British Caribbean, or the United States, and the details of who did the teaching also change with each story. It seems unlikely that Lewis recovered a true written language if this story is true, but rather that he at best fashioned a full script out of symbolic images similar to those that exist among the Akan. There has been some speculation that such a system of iconography could have survived if its original intention was to create a system of non-verbal warnings and alerts about the activity of the slave trade, giving it a logical relevance to life in slavery and an easy point of reference to share.

And of course a remarkable number of enslaved individuals did defy prohibitions on reading and writing in English too. The tightening of anti-literacy laws (which increasingly applied to free black people, as well, through the period) reflected in no small part the determination of many people to read and write. Through a mix of the manipulation of white elites (especially young children who did not understand the significance of the situation), stolen reading books, the efforts of anti-slavery preachers (particularly in the mid-19th century), matching spoken words to the text of newspapers and letters and various other ways, some enslaved individuals were able to gain varying degrees of literacy. Once one person had developed some level of functional literacy, they could also pass that skill on to their children or other trusted individuals within their communities. Whilst literacy could not become widespread under slavery, in being so hostile to the idea of black literacy, white elites also made clear that access to the written word meant power and a kind of freedom, and black communities - both enslaved and free - accordingly asserted their right to inclusion in that world of power and freedom when the opportunity arose.