BSD per se would exist without Stallman--it already existed before the GNU project. But it was non-free because it contained AT&T proprietary Unix code. Stallman was influential in getting the proprietary parts replaced and the BSD license fixed to be usable for free software. Without that effort on his part and the GNU project's (e.g. the AT&T C compiler was replaced by GCC), BSD today would be quite irrelevant if not outright dead.

I thought I had read that Stallman badgered the original dev of FreeBSD into adopting an open source license, but I can't find any references now. I probably misremembered, sorry!