Depends on whether demonstrated interest is a factor in admissions for this school. For some, it’s important and others it matters not at all. Google the Common Data Set for this school and look at the factors they use to make their decisions. (And check Section C while you are at it, if you haven’t already, to see how you compare to the admitted class. No amount of demonstrated interest is going to make you attractive if you aren’t in the target set.)
By the way, if you do send the email, it would also be a good opportunity to mention any new achievements and awards. And keep it brief. Adcoms are especially busy at this time of year.
No need to make up a story, if one school is your top choice and demonstrated interest is a factor you can email the adcom and let him/her know if you have had any achievements since your application was filed and that if admitted you will attend the college.