As a born and raised American, I'm inclined to think not. I could be wrong of course, but everything that I've seen and experienced growing up and living in the US has led me to believe otherwise.
I want to think that more protestors being armed would make a difference, but ultimately I believe it will just lead to escalation and more deaths by cop (and/or the national guard, as we're finding out in Louisville currently).
There's precedent for this. In the 60s the black panthers open carried in California to protest, of course, police misconduct. Reagan signed in the Mulford Act [1], banning open carry in CA.
If BLM want stricter gun control laws (not sure if they do), all they need to do is arm themselves at protests.
Apparently they were let in, then arrested, then released without charge and their guns returned as they hadn't broken the law. However, they were there protesting against the 'Mulford Act' that intended to disarm them, and it was subsequently passed. So they didn't get shot, but they didn't get what they wanted either, and they did get banned from doing it again.
Of course, there's a lot more detail than I've put into this post, and society was pretty different at the time. Reagan supporting gun control? The NRA as a sporting organisation that supported gun control? And the panthers were Marxist? So I'm not sure it's a very instructive example about how the same thing would go today.
[1] https://en.wikipedia.org/wiki/Black_Panther_Party#Protest_at...