That's been on my list of things to test for a long time now.
It shouldn't be that difficult to design and execute a reasonably trustworthy test for this theory.
Looking backwards, I do note that on 22 June I converted thousands of outbound links on about ten sites from nofollow links to dofollow links. Traffic on one site increased, traffic on another site decreased. There has been no noticeable change in traffic on the other eight sites.