Yes, they do.
There are also similar cages which omit the ear protection in favor of a lower profile, which I personally prefer. I think that either type is a good piece of gear to have on hand.
I'm not up on the insurance requirements of PB cert fields though, so ask around before you commit. Lump all available funds into good eye/ face pro right off the bat, and if you are going to be playing on fields which require PB Cert safety gear to play, you'll want to dump that extra $15-$30 into your pool rather than divide it between systems.
People always balk when I tell them to spend at least
$100-$150 on goggles, but I've been through enough systems for both Paintball and Airsoft to know that if you don't spend that much to begin with, you'll spend it over the fist season and STILL have to drop that much on the set you end up wanting/ needing.
Do lots of research, ask around, and make an effort to try before you buy (fitment/ comfort is huge
; don't automatically take someone's word as absolute truth or think that because a system is expensive that it will work for you).
Also, eye/ face protection should be regarded as disposable from the get-go in order to avoid heartache.
Good stuff may last 3 seasons or 10; but it needs to be replaced at the first goddamn signs of damage
Inspect your eye pro regularly. After every solid lens hit under ~30ft for paintball, after every nasty burst from a hot Airsoft gun.
Remember, military spec lenses may be able to stop a .22, but they're only rated to stop ONE .22. They may stop more, but if there are chips, gouges, cracks, or exposed faults after an encounter STOP USING YOUR EYE PRO, THROW IT AWAY, AND BUY NEW.
You only have two eyes.