[...] Perl accepts  m'^a$q' which can never match... unless  /m is somehow implied [...]

With or without the /m modifier, it can never match against any string whatsoever because as the regex is defined,  $ is required to match before something other than an end-of-string or newline:  'q' follows it in the regex.

If the regex is defined with a newline to follow the  $ metacharacter, if the  /m modifier is used and if the interpolation-suppressing  ' (single-quote) character is used as the regex delimiter, then a match is possible against a string with an embedded newline:

>perl -wMstrict -le
"my $s = qq{a\nq};
 print $s =~ m'^a$q'    ? '   ' : 'NO ', 'match';
 print $s =~ m'^a$q'm   ? '   ' : 'NO ', 'match';
 print $s =~ m'^a$\nq'  ? '   ' : 'NO ', 'match';
 print $s =~ m/^a$\nq/m ? '   ' : 'NO ', 'match';
 print $s =~ m'^a$\nq'm ? '   ' : 'NO ', 'match';
"
NO match
NO match
NO match
NO match
   match
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