No, BuddyPress is a plugin for WordPress itself. It would not work without WordPress Installation. After Installing WordPress, you would have to install the BuddyPress plugin.
Can You Create Buddypress Without WordPress?
Update on March 17, 2020
No, BuddyPress is a plugin for WordPress itself. It would not work without WordPress Installation. After Installing WordPress, you would have to install the BuddyPress plugin.