As you say, applying backstay tension on stiff masthead
rigs tends to tighten the forestay.
However, on boats with lighter, more flexible mast sections the backstay adjustment can put enough compressive loads on the
rig to bend the mast (imagine compressing a toothpick between your fingertips). This is esp. true with powerful adjustments like hydraulics.
On such
rigs checkstays are required to limit mast bend so that further tension does indeed tension the headstay, after the main has been flattened with bend.
You'll likely find such
rigs only on boats that were intended to be raced.