When running deployed services, you can deploy to the same port and differentiate which service receives the message using the base path.
In a recording situation, however, the answer is 'no'. The recorder listens on what amounts to a base path of "/". The recorder takes the incoming URI records it and sends it on to the provider endpoint.
The recorder wizard has no configuration allowing the recorder to accept requests matching a specific base path or URI while ignoring others.
This is one reason the recorder cannot record on a port where a virtual service has already been deployed into VSE.
If possible, can you declare a range of a few ports dedicated for recording only?