This is a compelling argument for posting to LinkedIn groups and I've little doubt that numerically, it's probably true that you can drive a fair deal of traffic by employing this approach.
We certainly see the number of reads a post receives increased significantly when it's shared to LinkedIn groups. However, the approach works best for our users when the individual professionals share to their LinkedIn groups; not just leaving it to the marking department to post under the company name.
Each group shows you the total number of members. Multiply that number by 1% and this should be your expectations of the number of new visitors headed to your website. If you post to three groups and each group has 10,000 members, then you should expect to get 300 new visitors to your site every time you post. Do this weekly and you would be looking at an increase in site traffic of 1,200 visitors. If your site only gets 1,000 visitors a month, you just doubled your traffic in 30 days with this one simple tactic.