Yes, each dice roll is i.i.d, so you can choose to look at it as 300 random samples of 50 throws each, or any other choice of N. Put another way, what you have

Yes, each dice roll is i.i.d, so you can choose to look at it as 300 random samples of 50 throws each, or any other choice of N. Put another way, what you have is 15k dice throws, and the fact that they were thrown by 15k, 5k, or 300 people can be ignored, if you choose to. In fact, it may be useful to 'shuffle' dice rolls into new 'samples' - that gets in to the use of resampling and bootstrap techniques. And also yes, for CLT to apply, each sample must have the same N.