Is there a quick & easy way to check if a module is pure-Perl, or is Perl+binary for both CPAN and core modules?

No. Well kinda. Sure-fire-way is to look at he source.

Cheap tricks

$ perl -MCGI -MDBI -le " print for grep /CGI|DBI/, keys %:: "
_<DBI.c
_<DBI.pm
_<DBI.xs
_<C:/citrusperl/site/lib/auto/DBI/DBI.dll
CGITempFile::
CGI::
DBI::
_<C:/citrusperl/lib/CGI/Util.pm
[download]

so DBI.dll/DBI.xs/DBI.c means DBI is binary, lack of .c/.xs/.dll/.so means CGI is pure-perl