Should the data be shuffled on a translation dataset
Yes, in NMT data is always shuffled.

For training, if each batch contains the same "type of content" (e.g. domain, register), then your model will be biased toward the type of content of the last batches. You don't want that. Apart from that, in NMT data is normally bucketed by length to avoid wasting batch space with padding.

For the test data, you would like to have data that follows a similar distribution to the one to be used in production. If the test is biased to only one domain, then you won't be able to assess correctly the expected performance of the model.

Document-level translation has little to do with the shuffling of the data. In document-level MT you normally have context sentences that are either ingested with an auxiliary encoder or as part of a single, longer sentence. This may reduce the number of sentences you can fit in the batch, but each sentence (+context) is independent from the rest.