I think the answer is "maybe"
Some areas of the country are very competitive for a nomination and appointment . . . so competitive that the Senators and Representatives of that state (or state region) coordinate their nomination picks, and agree NOT to duplicate nominations in order to ensure each of the worthy candidates receive a nomination. This has happened in Virginia, especially Northern Virginia, in the past. The Academy admissions office is usually made aware when this is the case.
To be appointed, you need a nomination. Whether you are appointed, depends on the quality of your record in comparison to those on the Congressional nomination slate of which you are a part. It's not so much how many Congressional nominations you have, but where you rank in that group of folks nominated.
Typically up to 10 names are put forward by the MOC. The MOC may designate a "principle nom" and then rank order everybody; or designate a "principle nom" and leave it up the the SA to rank the rest; or the MOC might just submit up to 10 names and let the SA due the ranking. So, if you have multiple noms, it is possible that it helps you by you being ranked higher on one nomination slate vs the other. (On the "competitive" point -- this is the key geographic factor. You may be the #1 Principle Nom from State Congressional District "X" -- but your record may not be as good as the candidate from State Congressional District "Y" that is ranked #10 on his or her MOC's nomination list. You get the appointment because you are #1 from your area or slate, but the person with a better record from a different place or on a different MOC slate does not get in.)
In addition, MOCs are restricted as to how many folks charged to them can be at the SA at any one time. I believe the number is 5. So, by having more than one Congressional Nom, you could have an increased chance for appointment if one of the MOCs that nominated you had more open spots at the SA than the other MOC that nominated you.
In summary , I think it is a "Maybe" and I do not think Admissions necessarily tallies up how many Noms you collected. Others may have different or updated data.