No it doesn’t.
The tank/Afv versions of the mg34 had an armoured sleeve to protect the barrel from shrapnel etc. Look the the one on the bow plate. It’s the same design.
You’re all thinking of the light role infantry one with the perforated outer sleeve to aid cooling/protect hands.
The co-ax mounted one was removed and put on the cupola where air threat was higher.
I used to build Tiger tanks exclusively about ten years ago and have spent 20 years in the British Army as part of the machine gun platoon/Corps of Drums.