Hi John,
Firstly, the kind of actention (or attention but for my recognition of a
requirement that what we do, think, and feel be understood on a common
concEPTual ground :>) that a placebo pill implies, is, by any reasonable
definition, cognitive.

Boosts of beneficial beliefs can surely be had from "precisely put and
positive words produced via a tongue" as much as placebo-pills can be
placed on a tongue and swallowed (given a properly prepared
placebo-promoting attitude) to some pain-controlling/blocking, hence
relatively health-giving, effect.

It is only anecdotal, but it makes sense, that by whatever way that a
person is made to feel less listless or more alert and to have a
positive outlook on life - as opposed made to feel inferior or
inadequate - would tend to make them 'underperform' in test of all kinds
of intelligence.

IOW, it seems reasonable to me that placebos ought to be able to affect
the cognitive performance of at least some people - only less so (or not
at all) on people that are not easily (or not at all) hypnotizable.