The <ConnectionStrings>
section shown above the <SessionState>
section is in NO way connected to sessionState. The ConnectionStrings section is for other purposes like when you have your own Database and you need to connect to it as well as this section only contains the details of database used for MemberShip, Profiles etc.
The <sessionState >
element has its own settings for specifying the connections string named: sqlConnectionString
as seen below:
<sessionState mode="Off|InProc|StateServer|SQLServer"
cookieless="true|false"
timeout="number of minutes"
stateConnectionString="tcpip=server:port"
sqlConnectionString="sql connection string"
stateNetworkTimeout="number of seconds"/>
Now when you use mode="InProc", then there is NO need to set the sqlConnectionString setting. Even if it is set, it will not be used as the Mode is "InProc" & not " SQLServer"