It depends!
For most electrodes, the brain doesn't really incorporate the implant. When a single electrode is inserted, you can start recording as soon as the contacts are inside the brain (in practice, you wait a few minutes since the brain is slightly elastic and stuff moves around). In humans, this is how deep brain stimulation is done--the surgeons use the neural activity to figure out when the electrode is in the right place. For larger implants like the Utah arrays, the insertion is a bit more traumatic. Allegedly, you get a pretty good signal right away, then inflammation makes it degrade for a while, and after ~12 hrs, the signal returns. However, the animal/patient is usually recovering during this time, so it's moot.
These electrodes are usually silicone and metal, usually tungsten, platinum/platinum iridium, or iridium oxide, so the brain doesn't really "accept" them. In fact, it tries to encapsulate and reject them, which limits the lifespan of the electrodes. In my experience, a two week old array might have nice, well-isolated neurons on more than half of the channels; after two years, you'd be lucky to get single units on more than a handful of the 96 channels.
However, there's a lot of interest in developing coatings that inhibit this immune response or actually encourage neurons to grow into the array. There's a lot of promising research on this, but nothing (as far as I know) that's commercially available.
As for the number of sensors...it also depends. You can do a lot with a 96 channel array implanted in the right spot, including spelling (https://elifesciences.org/content/6/e18554#bib27) and control of a robotic arm (http://www.jhuapl.edu/prosthetics/scientists/neural.asp) though neither of these is anywhere near "native" performance yet. More electrodes might help, but there's also probably some low-hanging fruit in figuring out the right control paradigms, decoding algorithms, and even where the electrodes are placed.
For research though, more and better arrays would be great. Many brain areas have a spatial structure. In visual areas, for example, cells representing neighboring spots in the visual world[0] are also near each other. Motor and sensory cortex also have a foot-to-face progression. Bigger arrays might let us sample from a more diverse population of neurons at the same time, which could be scientifically interesting and useful for BCI. Denser arrays might also allow for better recordings from single neurons. If you have a sufficiently dense array, you can record the activity of one neuron from multiple sites--this lets you isolate its responses better (this trick is commonly used with bundles of four wires, called tetrodes).
I would also love to get my hands on arrays made from multiple materials. Platinum is great for recording the activity of single units, but lousy for stimulation; its low charge injection capacity means that high stimulation currents damage the electrodes and/or nearby cells. Iridium oxide has a much higher charge injection capacity, but lower impedance and thus, fewer well-isolated cells. A "checkerboard" pattern of Pt and IrOx electrodes would be awesome, but is apparently difficult to make (no chance you run a fab, is there?)
The flips side of all of this is that amplifiers and ADCs are expensive (though much cheaper than they used to be), and adding channels rapidly increases the data files' size too. My experiments generate about 1 GB/minute, and we record 5-8 hours a day, 6-7 days a week.
What else? :-)
[0] The organization is really "retinotopic", meaning that cells receiving inputs from the adjacent parts of the retina are near each other in the brain.