Not on its own, no. Core BuddyPress activity updates are text (plus @mentions and auto-generated link previews if you’re running a link-preview add-on), no native photo or video upload button. To get real multimedia in status updates, you need an add-on.
rtMedia: The Established Option
rtMedia is the plugin most BuddyPress sites reach for. It lets members attach photos and videos to activity updates the way Facebook does, organizes uploads into albums with privacy controls, and works across profiles and groups. Active, 7,000+ installs, updated within the last week as of this writing.
Worth knowing before installing: reviews are mixed (3.7/5), with a real split between people happy with the free core feature set and people frustrated by premium pricing or support response times. Test it on staging and decide if the free tier covers what you need before committing to the paid add-ons.
The Other Path: BuddyBoss Platform
If you’re building on BuddyBoss Platform rather than plain BuddyPress, media uploads in activity updates come built in, no separate plugin needed. That’s one of the real differences between the two platforms worth factoring into a choice if you’re still deciding which to build on.
A Different Product Entirely
One correction: an earlier version of this post described “BuddyPress Status” as the answer here. It isn’t, that plugin adds a 140-character mood/status line with an emoji picker next to a member’s name, closer to old-Twitter than to photo or video sharing. Real plugin, active (v3.3.0, $49-129/yr), just not what answers this question.