I did not say that nicotine increases acetylcholine. Where did you see me saying that? Since it is an agonist of the AChE receptors it is expected to trigger a feedback mechanism and it seems that it does that - i.e. increases levels of acetylcholilnesterase, which breaks down acetylcholine.
http://www.jneurosci.org/content/jneuro/3/4/871.full.pdf
So, yes, nicotine exposure should lower acetylcholine levels but nicotine itself is a powerful agonist of those same receptors and the net effect is probably still heavily cholinergic. This is probably one of the reasons Big Pharma had (misplaced) high hopes for nicotine as treatment for Alzheimer and it badly failed in pre-clinical trials.
I wasn't directing it at you when I said:
I think that most people in general have the idea that ACh increases cognition and nicotines pro cognitive effects must stem from increasing ACh. I've seen that claim many times on reddit etc...I think that to say nicotine increases acetylcholine may not necessarily be true just because it is an agonist of nicotinic acetylcholine receptors.