I don't understand how this is going to help your applications. "Update letter" implies you have an update. Where have you interviewed? Or are you still in radio silence?
Without an II, you should update whenever it is a significant accomplishment. I don't know what you mean by a "brief, non-repetitive summary" of your secondary application. Every secondary is different. Every mission is different.
I guess you're doing a "check-in" pointing out "have you read my application?" Usually the answer you'll get is "yes we've screened your application." So then, what's next?