BuddyPress.org

No, I believe they do need dedicated. BP does not run well on a shared server. I have had a Hostmonster rep tell me they throttle all BP users and so do most other shared hosts. You may be able to run for a little while but soon you will get throttled and your site will slow to the point where it is almost unusable. You simply are not going to be able to run any real social network for $20 a month.