Applying to boutiques

If you are talking about the elite boutiques (Lazard, Evercore, Moelis, Greenhill, Perella Weinberg, Qatalyst, Centerview, Rothschild, Blackstone etc.), that is probably inadvisable since those places have recruiting protocols through campus recruiting and sometimes even online apps. If you are not at a target school, I guarantee that you will have a near 0% chance of getting interviewed unless you are lateralling over from another firm. Boutiques just don't have the resources to recruit outside of target schools and vet you. Don't mean to be mean, it's just a fact. If you are at a target school, you will do yourself more harm than good by emailing your resume out of the blue. So you do have something to lose. In the worst scenario, you could get blacklisted for annoying an MD.

In general, it probably makes more sense to set up a phone chat asking for information, even through a cold email, talk for 20 min, and then send your resume/cover letter. This should be done with employees at the analyst/associate level, not MDs. Invest in places that you have a reasonable chance of getting into. If that means tier 2 or regional boutiques, so be it. Good luck!