Depends on how $B::var was declared...
package B;
use strict;
my $nope = 0;
our $maybe = 1;
use vars qw($probably);
$probably = 1;
package A;
use strict;
print $B::probably;
print $B::maybe;
print $B::nope;
This ends up printing "11"... no zero. No error either.
Thus: Stuff that's really supposed to be shared by package B will be shared. %)
Can you give a little more detail on what you're trying to do, and how it's failing to work?