I've been trying to figure out whether this is true or not, and I've only been able to find that it doesn't compound: the noise from the original quantization and the noise from the second (post-resample) quantisation aren't independent, both arise from rounding the data to the same 16-bit grid. Somehow, this seems to mean the noise doesn't compound.

I wish I understood this better and at least knew whether it's true or false. I have to do more reading on it.

Sure, but you will resample ~5 times max.