I find it quite surprising that \"$a" creates a reference to an lvalue, since "$a" isn't an lvalue. This might be a bug, or an artifact of the implementation of perl. Unless I'd find a place where this is documented, I wouldn't count on it working on a next version of perl.

If I want a scalar to an anonymous scalar, I use:

   \do {my $foo};  # Or do {\my $foo};
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which is an well-known technique, and before we had auto-vivifying filehandles, similar to how we created references to filehandles (\do {local *FOO}).

As for sizes, \"$$" takes 2.5 times the memory \do {my $foo} takes. And even \"" takes more than twice the memory. This is because \do {my $foo} is just an SV, pointing to nothing. (The flag ROK says it's a reference). But \"" still has to point to something.

#!/usr/bin/perl

use strict;
use warnings;

use Devel::Size 'total_size';
use Devel::Peek;

my $a = \"$$";
my $b = \"";
my $c = \do {my $foo};

print total_size($a), "\n";
print total_size($b), "\n";
print total_size($c), "\n";

print "-----\n";

print Dump($a);
print Dump($c);

__END__
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25
12
-----
SV = RV(0x81c1df4) at 0x8191e58
  REFCNT = 1
  FLAGS = (PADBUSY,PADMY,ROK)
  RV = 0x8184180
  SV = PV(0x8184494) at 0x8184180
    REFCNT = 1
    FLAGS = (POK,pPOK)
    PV = 0x8189cf8 "23192"\0
    CUR = 5
    LEN = 6
SV = RV(0x81c1dfc) at 0x8191eac
  REFCNT = 1
  FLAGS = (PADBUSY,PADMY,ROK)
  RV = 0x8191f84
  SV = NULL(0x0) at 0x8191f84
    REFCNT = 2
    FLAGS = (PADBUSY,PADMY)
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