Drive shafts can wear out, but on RWD cars it's usually because the boots have failed and the grease has escaped rather than normal use.
FWD wear out because they are constantly working with both steering and suspension inputs.
In your case a worn drive shaft would clunk once as it takes up or releases load rather than causing a vibration.
If the gearbox mount has failed, incredibly likely given the mileage and the car has seen any oil leaks then you'll be able to push the tail shaft up and sided to side by hand. Be warned though, if the gearbox mount has failed then the engine ones won't be far behind... These split, lose their fluid then tear away... Symptoms start with NVH and end with the engine moving sideways 5-10 centimetres during hard cornering... This ultimately manifests as a noticeable shift in the CofG of the front end and a loud clonk when it hits whatever is next to it.
NVH during driving is almost always drive train mountings.
Collapsed diff mounts will give similar symptoms to the engine mounts except the diff is lighter so the clonks are quieter... You can still feel it move though under extreme load.