No, that is wrong. Satisfying strict depends only on the compile-time effect of my, for which its mere presence suffices. However, a conditional prevents its run-time effect of allocating a new scalar for that lexically scoped name, so that the name remains associated with the previously used variable. Observe:

use strict;
use warnings;

sub remember {
    my $memory if 0;
    print "Previous value of \$memory: $memory\n";
    $memory = shift;
}

remember "foo";
remember 42;
remember "bar";
remember;

__END__
Use of uninitialized value in concatenation (.) or string at - line 6.
Previous value of $memory: 
Previous value of $memory: foo
Previous value of $memory: 42
Previous value of $memory: bar
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This if 0 hack has been known for a long time and might even be useful if it weren't such a dirty trick. An actual condition in that place nearly certainly means that someone is going to be very surprised.