I would say SOMETIMES it could affect your ranking, at least Google+ for Local Businesses in Googles's local based searches. I tend to see local businesses with more reviews, and a higher overall rating fair better than those with none. But then again I have also noticed it depends on the location as well. For example, one of my clients is a local business in my city. I have noticed that a few competitors who are very close to my house (less than a mile away), who have google+ business pages with 0-2 reviews show up in the local results on page one of Google for main keywords, while competitors 10 miles away with 20-100 positive reviews on their Google+ page are mixed in, outranking the business 4-6 miles away with 6 reviews and a high rating. It's not random as I always see the same businesses on their when checking my clients ranking. It does change once in awhile, but rarely and not by much. I am sure there are many other factors that play into that as well...I mean. It's Google.
On the other note When it comes to leaving reviews on sites like Yelp or Foursquare, sometimes a fresh IP isn't a guarantee win as those bigger sites are familiar with that type of thing. Make sure the IP addresses are close to the business, or at least in the same county. Could look fishy if people with IP addresses in NY and Miami are leaving are leaving reviews for a local business that in San Francisco. Also, if the site has the option to "check in" to a place I will use android phone emulator, or spoof the location on phone so I can actually check in to the business. It should give the review a better chance at not being filtered out. Just my opinion at least.
Also, good reviews are great at getting business to your client (or yourself) especially on Yelp, and that absolutely affects how your business ranks there. Also, Google+ is known to gather reviews from other reputable local citations to attach to your Google which is great.