The simple answer is No, you should not use a plugin to build back-links.
There are some great WordPress Plugins out there that help you with tracking your back-links, I suggest the MozLinks one, it's great. But it monitors your work, it doesn't do it for you.
Much like their brick and mortar your client needs to understand that business online is business, all the same. You wouldn't trust a script written by a shady company to hire your employees or automate your accounting, you should not take such a route for building your site either.
Automated scripts are a clear violation of the Google Webmaster Guidelines (and the other search engines too) http://goo.gl/bdca8 you can read it on their site.
The other thing is, automation means no control. You can end up linked to bad neighborhoods like porn and RX sites as well as get de-indexed and not show in the SERPs at all.
What to do? Put your efforts on building a purpose for your site. Provide value in its vertical that is unique and useful. Build links when you find others that have done the same and ONLY link to sites when you are willing to put your reputation on the line for them, as in a way that is what you are doing.
Want more visitors? Answer one question.... why?
Why would someone want to visit your site? Ask it everyday and answer it in a new way and you will have more traffic than your shared hosting plan will allow.
