In a word: No.
I spent last night compiling data from 2011 thru 2013 for all of my book sales. I have done several of the Amazon Kindle Select giveaways for a few of my titles over the years, at -best- a giveaway will not hurt your sales. However I see no data at all to suggest that giving away a book will help sales of that title, and quite a bit of data that seems to indicate that it will actually -hurt- your sales of that title.
Note that I am not talking about 'loss leaders', which for example would be the first book in a series sold cheaply or for free in order to entice readers to buy the rest of that series.
I also have noticed that in the majority of cases all titles sold the most number of copies in their first year of release. Only in two cases was the peak year the second year of release.
It also is apparent that a new release does impact sales of already existing titles in a positive manner, so the old adage to 'keep writing' is a true one.
Every quarter I transpose all of my sales data for each title and sales channel to a spreadsheet, each year I start a new spreadsheet. It's a pain in the butt at times however it does help put things in perspective. My first year's sales were low, I didn't start publishing until April, and did not publish a lot of titles. My second year I saw my sales increase by a factor of ten, but I also published 12 titles that year, mostly novella's and two short story collections. While I published less in 2013 than 2012 I sustained my sales numbers for that year.
From a 'cost benefit' analysis, novellas and novelettes are the best bang for the buck, you can write them in a week (including editing), while a novel takes months to write and you can not sell it for all that much more than a novella/novelettes - say twice the price for ten times the work. I am giving a lot of thought to changing my approach on novels and writing them as a serial, releasing them in 10K to 12K segments. Current research by booksellers tends to indicate that 70 percent of readers -want- series type books.
What I have also found to be very interesting is that the majority of my readers have actually -left- amazon and moved to B&N or Kobo/Smashwords. Currently ~70 percent of my sales are on B&N, ~20 percent is Kobo/Smashwords, and Amazon accounts for only ~10 percent. This may be because I also write PNR novellas (under a pen name) and B&N has a bigger PNR audience after Amazon's 'erotica purge' which did drive quite a few PNR and Romance writers off of Amazon (and their readers by association), but that's another story.
I hope some may find this information to be useful.