Yes, that's completely incorrect.

First, "g" doesn't do that at all. It means (more or less) "all instances".

# Check for a match
if (/pat/) {
   ...
}

# Find all matches
while (/pat/g) {
   ...
}
[download]

Second, that's not how regexps match at all.

print( 'abc' =~ /b/      ?1:0,"\n");  # 1
print( 'abc' =~ /^b\z/   ?1:0,"\n");  # 0
print( 'abc' =~ /^abc\z/ ?1:0,"\n");  # 1

print( 'a2b3c' =~ /(\d)/     ?$1:0,"\n");  # 2
print( 'a2b3c' =~ /^.*(\d)/  ?$1:0,"\n");  # 3
print( 'a2b3c' =~ /^.*?(\d)/ ?$1:0,"\n");  # 2
[download]

References:

• perlop (m//, s/// and qr//)
• perlre
• perlrequick
• perlretut