Hello, Veeam Backup performs license verification against ESX hosts when backup job is runnning. Before backing up every VM, Veeam Backup looks up if ESX host for the corresponding VM is already present in the list of licensed hosts. If the host is not present there, it is added to the list. So, the only possible way for newly added ESX host to affect Veeam Backup licensing, is to backup a VM running on it.
In any case, even if this happens accidentally, you can always resolve this situation immediately using the Help | License information
dialog in Veeam Backup interface. This dialog lets you review currently licensed ESX hosts, and revoke licenses from unneeded hosts.
By the way, please note that whenever you need help ASAP, it is best to contact our support instead of posting the issue on forums. This forum is not constantly monitored on weekdays, and is generally never monitored on weekends. I am just stuck in the city this weekend because of family reasons.