I found this "video" on youtube by chance.  It is a recording of Eduard Melkus (Violin) and Caro Atmacayan (Cello) or Capella Academica Wien made in 1973.  Of course the violin playing is really "old school," but I was really surprised to hear the cellist realizing some of the figures in the bass.

The reason for playing chords on the cello and not using the harpsichord comes from the title of Corelli's Opus V violin sonatas: Sonate a violino e violone o cimbalo.  If we interpret the title literally, we should accompany the violin with Cello (violone) OR harpsichord.  The question that naturally follows is, "If the accompaniment is cello alone, should it make a realization of the figured bass?"

I think it is not a bad realization on the cello - I find that the possibilities of realization on a cello are quite limited when maintaining good voice leading.  More than 20 years after this recording you have the Corelli Op. V recorded by John Holloway, Lars Ulrik Mortensen and David Watkin, c. 1996.

David Watkin wrote a very interesting article, "Corelli’s op.5 sonatas: ‘Violino e violone o cimbalo’?" in Early Music, Vol. 24, No.4 November 1996, pp. 645 – 663.  This covers the whole issure in more depth.