No, "Bernie Bro" is in some ways, similar to the original usage of SJW that's being discussed in this thread. Bernie Bros are typically white young men whose support for Bernie Sanders outweighs their commitment to human decency.
Remember when people were criticizing Bernie for not recognizing Black Lives Matter? Which, ended up being a net positive as it really improved his approach to those issues. However, during that time, a large number of Bernie's white supporters were harassing the members of Black Lives Matter for, as they claimed, not recognizing that Bernie was their best option, and that they should just shut up and support him.
Those are Bernie Bros.