Yes. This has always been the case. Even prior to 1964, HBCUs admitted white students, but most didn't want to attend (still don't; we don't bite, promise). HBCUs routinely admitted non-white students who weren't black prior to 1964, too.

HBCUs started because blacks were not allowed to attend white schools, not the other way around. If you were black and were among the few who were admitted to white schools, you got treated like shit.

Typically, if you were black and applied to most non-HBUCs prior to 1964, you were generally rejected for being black.

Without HBCUs, the black middle class wouldn't have even existed.