None at all.

If were taking down the distributor, then yes, the log would grow. You're not. You're moving one of the subscribers. The publisher won't even notice because it doesn't care whether or not there are any subscribers at all, if they're up, down or anything else

Transactional replication is publisher -> distributor then distributor -> subscriber.

Providing the period that the subscriber will be disconnected is less than the retention period for the replication, when the subscriber is reconnected it will catch up. If it's disconnected for longer then the subscription will be invalidated and will need to be re-snapshotted.

So, no. There's no grounds for the sysadmin's concerns. Providing the distributor is up and the log reader running, the log on the publisher will be properly truncated at the usual points.