Setting up Drupal without a domain name
Ok, the answer is unfortunately Drupal can not handle this situation. What should be done is the following:

On Windows

Go to: C:\Windows\System32\drivers\etc 

Open: hosts file

Add at the end: 

100.200.10.20 yourdomainname.com
109.200.10.20 www.yourdomainname.com


On Mac

Open Terminal (Applications -> Utilities -> Terminal) 

Open hosts file: $ sudo nano /private/etc/hosts 

Type your user password when prompted 

Add at the end: 

100.200.10.20 yourdomainname.com
109.200.10.20 www.yourdomainname.com


Save the file Flush the DNS cache: $ dscacheutil -flushcache

NOTE: The IP is the IP of your server. You can get it by logging into Plesk, Home>System Overview