I would suggest not, based on the RFU's performance in the last few years !
If you want a professional job done, employ professional people to do it. Headhunters help make objective, measured decisions based on a clear specification and set of selection criteria.
I know my business inside out, and most of the people in it, but I employ headhunters to help me specify the role and its context in my organisation, find & screen potential senior employees, and help me make the final decision.
On their track record I would suggest the RFU are the least qualified!
Odgers have a pretty good record. They were involved in Roger Lewis going to the WRU and he seems to be doing a pretty decent job there. They should have probably used them to sort out the Chief executive role!