Is the connotation of "naughty" always sexual?

Solution 1:

Of course it's not always sexual. Here are a couple of dozen instances of "a bit naughty of me", within which I can't see that many (if any) have sexual connotations.

Context is everything.

Solution 2:

To answer your first question:

Does the word "naughty" always have a sexual connotation if it is used between adults?

The answer is "no" – the word need not always have a sexual connotation.

That said, the word is often used to indicate some kind of misbehavior: disobedience in children; suggestive flirting or morally questionable behavior between adults. If you browse through the Wordnik entry for naughty, you'll see meanings like these strewn about:

adj. Indecent; improper: a naughty wink. Archaic Wicked; immoral.
Morally bad; wicked; corrupt. In a mitigated sense, bad in conduct or
speech; improper; mischievous: used with reference to the more or less
venial faults or delinquencies of children, or playfully to those of
older persons: as, a naughty child; naughty conduct; oh, you
naughty man! adj. bad; tending to misbehave or act badly. adj.
risqué: flirting with impropriety and/or bad taste; morally dubious,
especially sexually suggestive, usually in a mild way. adj. evil,
wicked, morally vicious.

In short, the word itself seems loaded with enough innuendo that I think you ought to consider other candidates for your message.

Put another way, I could design a smart phone that opens a texting window with the message BEGIN INTERCOURSE. That's grammatical, and certainly within the scope of the word's definition, but still I don't think it's the best choice of words.

If you wanted to avoid lascivious connotations, I would think inappropriate would be a much better word than naughty: No inappropriate apps selected

Inappropriate is much more generic, and slides more easily into a broad range of contexts: inappropriate for work, inappropriate for school, etc.

Solution 3:

The word "naught," literally means "no" or "none."

To be "naughty" is to have "none" (or a lack of) some essential quality. It basically implies a short-coming or deficiency.

In my (New York) circles, on the other hand, to "no-no" someone is to possess them sexually. (That is, you do things to which people are supposed to say "no, no.") In that kind of context, "naughty" would have sexual connotations.