Not necessarily.
There was word going around like a year ago that Tesla was changing to thicker steel on the doors (and only the doors) specifically to pull a stupid stunt like this. It is reportedly 3mm stainless.
The claim is that they shot it with a 'Tommy Gun'. The Thompson Sub-machine Gun usually fires .45ACP, which is a relatively heavy and wide subsonic round in the standard loading. Non-jacketed (just the lead without copper) or hollow point .45ACP would be unlikely to penetrate 3mm of any stainless steel. Or most mild steel. We know this because the FBI famously switched from the Tommy gun to BAR because .45ACP wouldn't reliably penetrate Ford Model B body steel. This has more to do with .45ACP than anything to do with how 'special' the steel is. Any of the 'heavy/slow' handgun rounds are unlikely to go through.
What is? Basically everything else including the most popular handgun round by a mile, .9mm. And steel tipped .45. And high-velocity .22. And almost every single rifle round. Interestingly, a stainless steel breastplate over a quarter of an inch thick would be fairly good protection (apart from the spalling) against most handgun rounds. You know, if you want to walk around with more than 75 lbs of stainless steel around you rather than far less than half that in a hardened carbon steel, or AR steel, or aramid fiber, or even fiberglass, which all do far better.
Now there are plenty of reasons to be skeptical this was actually shot with a Tommy gun. The drum mag on one holds 100 rounds, and there are 69 dents in this. (That probably isn't chance because Musk is a child.) None of them overlap really, maybe two are closish. None show spalling (sideways gouging caused by the round becoming small pieces when it shatters against the steel), none show lead marks, none show powder marks. The distribution doesn't show rising or the normal spread of a Thompson. If this was shot with a Tommy gun, it was a semi-auto version from a decent distance with soft rounds or even half loads one at a time, slow aimed fire. And then cleaned with a pressure washer. Without being recorded.
Silly stunt is silly.