I'm not sure if I can follow you here, Iain, however, slow but not dumb could work for a Neanderthal, I guess.
The Broca Area, Wernicke Area, and Angular Gyrus are all present prior to Neanderthal. Not only is it clear to us that they possessed the brain areas needed to process language, but they also left behind cultural elements that allude to the fact that they communicated complex, abstract thoughts like what happens to us after we die, since we have found evidence of ritualized burial. This being the case, then, to the OP, a lot is going to depend on whether the Neanderthal in question was found as a feral, singular individual, or if this person was originally part of a group of Neanderthal people. If your Neanderthal comes from a group of Neanderthals, then he or she will have language already. Spoken language. All humans who can speak, do speak, when they are given the opportunity to exercise this facility with others who can also speak. We have never once found a culture that didn't have spoken language because spoken language is not an invention, it's a feature of who and what we are, as much as a hand is or a foot is. But, like any part of the body, if for some reason it doesn't ever get used (like if the Neanderthal child manages to somehow survive alone with no others), then speech in the future, even when it comes into contact with beings who do speak (us) may not come easily to him or her. If you have this Neanderthal grow up where it has contact with anatomically modern sapiens (you and I), and it has the chance to hear, process, and engage speech, he or she is going to speak just as readily as you or I. It won't sound the same. Different facial structure, different resonating chambers in the head, greater prognathism, different position of the larynx, but it's going to speak. You'll find in your research that the Neanderthal brain was in fact larger, on average, than ours. This DOES NOT equate to them being smarter. Different structures were emphasized in their brains than in ours. But, they were very likely smart enough to hold their own against the average Joe or Jane. tl;dr It's going to speak if it was given the chance to encounter and process language when it was young, and when the modern humans in your story engage this Neanderthal, this Neanderthal person is going to be a person.
Neanderthals also had the same version of a gene related to speech as modern humans do, whereas other species do not. It isn't dispositive, but it is evidence. "Other experiments Paabo and his colleagues have been running have offered more promising results. At the talk, Paabo described some of his latest work on a gene called FoxP2. Ten years ago, psychologists discovered that mutations to this gene can make it difficult for people to speak and understand language. (Here’s a ten-year retrospective on FoxP2 I wrote last month in Discover.) Paabo and his colleagues have found that FoxP2 underwent a dramatic evolutionary change in our lineage. Most mammals have a practically identical version of the protein, but ours has two different amino acids (the building blocks of proteins). The fact that humans are the only living animals capable of full-blown language, and the fact that this powerful language-linked gene evolved in the human lineage naturally fuels the imagination. Adding fuel to the fire, Paabo pointed out that both Neanderthals and Denisovans had the human version of FoxP2. If Neanderthals could talk, it would be intriguing that they apparently couldn’t paint or make sculptures or do other kinds of abstract expressions that humans did. And if Neanderthal’s couldn’t talk, it would be intriguing that they already had a human version of FoxP2. As scientific mysteries go, it’s a win-win." http://blogs.discovermagazine.com/loom/2011/11/14/neanderthal-neuroscience/#.WKeDOFX55QJ
