Correct. Having multiple nominations from the same or different nominating sources will not increase your WCS or improve your chances off the NWL.
What it does is give the academy additional options to grant you an appointment by giving them additional places to charge your admission against. For example your congressman may submit a ranked slate and he ranked you #3 on that slate (the fiend!). On your Senator's slate, which she submitted as competitive (best Senator ever), you have the highest WCS of anyone on that slate who was not already #1 on a different slate so the admissions team grants you an appointment and charges you against that Senator; that Senator's nomination got you in.
When you are not #1 on any slate: your WCS allows you to compete against all other applicants who are also not #1 on their slates so that the academy has some mechanism to fill out the class. That is the NWL.
This analogy may help:
You need an invitation to the party (nomination). Up to 10 invites can go out from any one person (MOC) but only one individual invited by each said person is guaranteed to be allowed to go in the door (#1 ranked). The line is ordered by how nicely you are dressed (WCS) or in the order where the invitation invited you (ranked slate). If the same individual is invited by different people, you may end up standing in a line with less than 10, or if you had multiple invitations, you can stand in different lines. If you are #1 left in your line, you likely will be allowed to go in. If someone else in your line goes in ahead of you, once they let in someone from all the other lines, they form a new line based on your overall appearance (WCS). Only people invited can stand in those lines regardless of how nicely they are dressed. They let additional people into the door who seem to be dressed the nicest in first. After that, they select some people out of the line, not based on how nicely they are dressed but because they need a truly diverse party where they have enough people with red hair (because they need the party to look like the population at large). Once the party is filled up, those left standing outside are told they were wanted but there just wasn't enough room in the party this year (TWE), but if they can dress nicer and get an invitation again next year - assuming they still want to come to the party - they can try again.
After you get in the party:
Once in the door, you find out it isn't a really a party and people yell and hold you accountable. You begin to wonder why you wanted to come in the first place because you are expected to clean and serve others at the party, but still find time to dance and play all the party games ("Beast" and Plebe Year). The first time you are allowed to leave the party you meet others who you know that were left outside. You find out they went back home and have since been attending parties where they are the guests and that they have been having lots of fun. The only reason you go back to the party is because you realize that those at your party that have been there the longest actually enjoy it, and because everyone else who came at the same time as you is having your experience but is getting by; you determine you can too. You also realize that all these things you are expected to do while at your party will help you become better at planning parties in the future - which is what you are really want to do and is why you came to the party in the first place.