Does it make sense to do train test split when trainning GANS?
Training GANs is only a partially unsupervised task, IMHO. It's certainly unsupervised for the Generator, but it's supervised for the Adversarial Network. So it might be useful to test the Disciminator's ability to distinguish fake and true cases on new data it has never seen before.

In other words, it makes sense to split your dataset in train(-validation)-test if you want to understand the Discriminator's ability to generalize its task on data it has never seen before. In case this is not of your interest, I guess you don't need to do it.