Interestingly, in the two versions of Perl that I have access to here, 5.004_04 and 5.6.1, this snippet

$_  = "aa";
$$_ = "bb";

print $aa;
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Notice the lack of my, and the lack of use strict; - it only works without strictness, which I guess was the point of the OP's question about turning off strict vars.

It's not a good thing to do, admittedly - though it would seem to be valid syntax, at least historically.

Updates to add a few words so that the post makes a little more sense.

Update 2: Just noticed that my $$_ appears in both the OP and in Fletch's reply. Doh. Fletch is right, of course, my $$_ = $_ isn't valid syntax.