No. Amazon does not publicize any search volumes data.
Relative Search Volumes of Sonar
As Amazon does not offer any kind information on search volumes, Sonar's data is based solely on Sellics' investigations. With the help of complex calculations regarding the probability of keyword occurrences and various other KPIs, Sellics is able to precisely determine the relative search volumes of keywords.
Vague Estimates of Absolute Numbers
In the US (amazon.com) 5 bars of Search Volumes can safely be interpreted as significantly more than 1 million monthly searches. In Germany (amazon.de) 5 bars may stand for around 1 million searches per month.
More & concrete information about this is currently not available.