Matt; what you say is "partially" true. There are 2 ways to receive an appointment. 1) From a nomination slate; and 2) From the national pool. So, the more slates you are own; e.g. 2 senators, 1 representative, presidential, vice presidential, ROTC, and some other military related slates; the more chances you have of receiving an appointment for that slate. Imagine it's like a lottery ticket. You only need one to win, but the more you have, the better your chances are of winning.
If you don't receive an appointment from the slate you're on, you will then be put into the national pool. Once in the national pool, it doesn't matter there how many nominations you received. It's simply your name, application, and a composite score. This is where you are simply racked and stacked against all others in the national pool, and the academy will take the amount that they need to fill the class. In other words, they give out the mandatory appointments first; one from each MOC slate submitted. Then, the academy chooses how many of the Presidential, VP, ROTC, and other military related to give appointments to. (Not to exceed the maximum number allowed). Then finally, they will take the remainder they need to fill the class, from the national pool. And for what it's worth, NONE of the appointments that come from the national pool, count towards a senator or representative's maximum of 5 constituents at the academy.
As for your senator/representative, each of them have a CHOICE on how to present their slate of 10 names. The can choose to simply give the academy 10 names and let the academy rank them and choose 1 for an appointment. The MOC could instead choose to rank their slate of 10 names themselves. If they do this, then the academy has absolutely no choice whatsoever in who to give an appointment to. As long as the nominee is 100% qualified, the academy MUST give the #1 person on the MOC's list the appointment if the MOC "Ranked" the list. Doesn't matter if the #1 has the lowest score of all 10 on the list. The 3rd method is a combination of the 2. The MOC list's their #1 choice, and the other 9 are ranked by the academy. So, if the #1 listed is 100% qualified, then the academy MUST give them the appointment. If they aren't qualified, then the academy can take from the other 9 based on their ranking.
Now there are some other variables. e.g. If the person given the appointment decides to turn it down, technically, the academy is suppose to go back to the list and take the next person. But I won't go into that here and now. That gets really complicated. But the answer to the OP's question isn't simply yes/no. That's because the question really isn't if it's better. The more nominations you get, the more chances you have at receiving an appointment. Again; it's like a lottery ticket. If you only have a representative, then you have "2" chances of receiving an appointment. That representative's slate, OR, the national pool if you don't get the rep's slate. On the other hand, if you have a nomination from the representative, 2 senators, a Presidential, a Vice Presidential, and an ROTC; then you have "7" chances at receiving an appointment. (The 6 I listed plus the national pool).