no you dont need to do this in Domain B
Anyway i would suggest it is much easier you define a conditional dns forwarder in Domain A DNS to the Domain B DNS, so you dont need to add all entrys in Domain A DNS.
Oh and while ADAudit uses the short names and add the Domains from Domain search list of the local machien to resolve Hosts, if you want to Monitor Hosts in Domain B, add to the ADAudit Plus Servers Network Settings (Windows) Domain B to the domain search list