Arequire- No. not necessary at all. But as so many just feel more comfortable with an AV on board there is no real reason not to use one. A good AV will just take the workload off of the Sandbox.
Formerly I really liked Qihoo, but since the company was taken Private they initiated a plan to have ads on the freeware version. Already implementation of this has caused some issues as new components have been sandboxed- this may not be a bad thing at all actually, but I've not had the time nor the desire to follow up on this so I have to refrain from comment.
Currently something like Avast or BD can be used as a supplement to CF without issue.