You evidently believe that the PSAT score will give a bit additional consideration. No one can with veracity say it absolutely will not , so go on ahead.
If AOs are thinking along the line you believe they are, they well know when the students can next test and if those scores don’t show up, possibly make assumptions down the path you are assuming. The PSAT score does not show up in any of their internal records sonI truly doubt they ‘ll give it a thought. I’ve known too many kids who did not live up to SAT expectations extrapolating upwards from PSAT.
With the number of apps these AOs have to process, it’s not going to be something to consider.
But when one gets a thought, an idea like this in mind, difficult to dispel so go ahead and include the score somewhere.