I suspect the limit of what can be expressed in human language and comprehended by the human mind is vast, but yes, not infinite. I think the AIs will absolutely saturate the connection between them and us, with a non-stop torrent of information which will range from useful to civilization-changing.

And I think this is all very unlike how we are currently impacting the lives of cockroaches with our insights about, well anything. Thus, it's not a good analogy.