In short no.
With a free agent frenzy going on right now it is easy to get excited about your team's ability to change it's fortunes. But does "winning" free agency help a team win. Check out this dashboard below that looks at free agency over the last 5 years and every team's change in record.
As you can see there is not a strong relationship between a team successfully acquiring the top free agents on the market and winning the following year. For example, the Falcons last year made a big splash in free agency signing 4 of the top 50 free agents. However, their regular season win percentage went from 81% in 2012 to 25% in 2013. This was due in part to injuries but it shows that success in free agency doesn't guarantee a great season.
Play with the dashboard and find out yourself.