You are totally overthinking it. If they want you, they'll rank you high. If they don't, then they won't. This idea that "showing interest" is somehow going to make a huge difference is, in my mind, very misguided. While it's unlikely to ever hurt an applicant, the benefit is nearly identical.
Think about it from the program's perspective. How many spots is "interest" worth on a rank list? Is interest worth picking a less qualified or less liked applicant? What's the benefit to them? Perhaps in an extreme case between an applicant who landed 7th on their rank list, and someone who felt their match was stretch, there may be some improvement in motivation, but internship is hard and people will trend towards their baseline eventually.
As a resident, I've received emails from applicants I've met who I absolutely did not want as a part of my program. Their interest in my program, no matter how superlative, is really not going to sway my opinion or what I'm going to tell my program director. In a way it's possible that my comments will be even stronger in opposition.
