The only time this will probably make a difference in a competitive specialty is if you’re being yield protected based on geography.
Let’s say op is from Florida. They lived their whole life in Florida and are in a medical school in Florida. Then they apply for residency in Michigan. While people do spread out, PDs also like to have residents who they know are happy in their program so they don’t have to deal with drama and such. Thus, they’d probably take someone from the Midwest with lower scores than Florida boy since it’s a sellers market and they can basically choose whoever they want. Now, let’s say Florida boy knows an attending who trained with Michigan PD. He calls him one day and says: “yo, you need to give my dog Florida boy an invite, he ****ing loves snow. He’s dying to just freeze his ass off for 6 months of the year.” Michigan PD might be shocked to hear this and give you a legit invite and actually rank you decently knowing that you won’t constantly bitch and moan every day about how damn cold it is for several years in a row. This is an example of the PD yield protecting their interview spots based on geography. Happens a lot actually, particularly in programs that are in “less desirable” locations.
Op, if you have a situation like that, sure go for it, it might make a difference. But having someone who went to Harvard email the PD at Harvard isn’t going to make you match at Harvard. Even if you get an interview there, you are going at the bottom of the list probably and their match list will end at the top whatever spots they have + a few. Just a fact, sorry. Maybe at some spot in nowheresville (which hopefully you applied for) but not at any big university where the PDs have god mode status.
So yeah, I’d personally just chill but I also have no idea what your application looks like or how many programs you applied to so who knows, maybe you should be panicking?