Apparently yes, from Wikipedia's OpenBSD entry (and this one):
Privilege revocation is similar and involves a program performing any necessary operations with the privileges it starts with then dropping them. Chrooting involves restricting an application to one section of the file system, prohibiting it from accessing areas that contain private or system files. Developers have applied these features to OpenBSD versions of common applications, including tcpdump and the Apache web server.
The article refers to the CVS log (this commit) for details. There is a mailing list discussion about this (which I haven't read), too.
Long story short, OpenBSD's
tcpdump from the base system is privilege separated already. (And I can't comment on their solution vs. Capsicum.)