Yes, I guess I was a little too unspecific in what I wrote: Given a string $x, looks_like_number($x) should accurately report whether the warning will occur.
Note that Scalar::Util::looks_like_number() is a different function. (That is, it doesn't simply wrap the perl API function of the same name ... it does some other stuff as well.)
True, it's a different function - AFAICT, Scalar::Util::looks_like_number just adds get-magic to Perl_looks_like_number in sv.c, which in turn calls Perl_grok_number in numeric.c, if the scalar has a valid string component (SvPOK). And my understanding is that grok_number is the same internal function that is used to inspect strings for their numeric content - see e.g. Perl_sv_2nv_flags in sv.c, which is called by the SvNV macro, and which calls not_a_number to generate the "Argument isn't numeric" warning.
I had done all this research in the past, and perhaps remembered it a little too simplified, thanks for poking me on this :-)
Update: Well, to nitpick: I did write "the exact internal function that Perl uses to check strings", and you didn't give it a string ;-P But "exact" is indeed inaccurate.