using port range for connecting to Postgres
No, that's not possible.  A single Postgres server can only listen on a single port. 

But: the communication through the port is not a bottleneck. 

For every connection made, Postgres creates a dedicated backend process once that is established the backend process does all the work. 

If you want to increase network throughput you could install a second network interface and make Postgres listen on both interfaces.

If concurrent use of a single server port was a problem, websites wouldn't be able to handle the load they can. After all a webserver only listens on a single port as well (80 or 443)