The order of your statements is deceptive. use happens at compile time, so your code actually runs them in the following order:

package Foo;

use base 'CGI::Application';
use Bar;

print "@ISA\n";
@ISA = ("Bar");
print "@ISA\n";
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The first print should be wrapped in a begin to have it exected at before the use Bar.

Same results in this case, but it's something for which one should look out, especially when demonstrating a point.