Can a Zero-Fee Transaction Be a Part of a ‘Batch’ Transaction?

A zero-fee transaction can be part of a batch transaction if the batch is created by the miner for their own internal purposes, such as paying out multiple addresses simultaneously. In this scenario, the entire batch transaction is essentially whitelisted by the miner.

For a user-submitted batch transaction, while technically possible, it is highly unlikely to be confirmed. The miner's selection algorithm focuses on the overall fee-per-byte of the transaction, and a zero-fee batch would not be competitive against any fee-paying transactions.