You certainly can just remove the plugin folder. There are no new database tables – only a single Options record.
More to the point though is why is there a problem. So you could check a few things first…
Firstly – is this using the very latest versions of WP, SP, BuddyPress and out BP plugin? I know there was a problem on a previous version that could show this behaviour if there was some setting in BP itself turned on 9i would have to search out the details).
Next – is the name of the folder the plugin is in actually named exactly ‘buddypress’ which it must be – and can you confirm that it was loaded into the correct SP Plugin location.
It could even be a simple corrupted file which does happen to everybody every now and then – especially if uploaded to your server using FileZilla.
That’s a good list for starters…