If your site is on the 1st page in search results , sure your traffic will be change. Try to buy google plus one
Yes if you share daily updates regarding your website in your Google+ brand page so, definitely you get better result with your website traffic.
Yes it will effect if you keep updating your status. The rate of traffic will depend upon your activities and sharing. The more you interact, better will be the results. But as the traffic on Google+ is not as huge as FB, don't expect miracles. Now a days Google has focused primarily on Google+, hence the initial boom was because of their advertising on the very first page of gmail. Anyway, you can create a profile for the company and carry on with some regular activities, because you never know what Google may come up with.
small Article on GOOGLE PLUS : http://www.searchenginejournal.com/search-plus-your-world-twitter-google/38649/