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Can worn rear differental mounts cause damage to the transmission if left too long before replacing?

We'd really need to know a bit more about what has happened and why.
Generally speaking, worn diff mounts would be unlikely to cause damage to the transmission as any slack should be taken up by the driveshaft universal joints, but wear to this extent would normally be felt through the driveline. If the vehicle has been on the road and passing WoFs, it's unlikely the wear would be this bad and although you don't state the mileage, as the vehicle is not all that old, I wouldn't think the diff mounts would be worn to the extent that they could cause damage.

Hi my Rav4 has a very low 24, 000km for its age.
I have noticed a slight clunk sound coming from the rear when I accellerate from a standing position and have been told that it could be caused by worn diff mounts.

At 24,000km I'd be very surprised if the diff mounts are worn or if there's a transmission problem. It could be something as simple as a loose road wheel, but the best advice is to have your mechanic put the vehicle up on a hoist and check the driveline, including all mounts, universal joints, bushes etc.