No.
http://msdn.microsoft.com/en-us/library/system.data.sqlclient.sqldataadapter.aspx[
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Note that the code does not explicitly open and close the Connection. The Fill method implicitly opens the Connection that the DataAdapter is using if it finds that the connection is not already open. If Fill opened the connection, it will also close the connection when Fill is finished. This can simplify your code when dealing with a single operation such as a Fill or an Update. However, if you are performing multiple operations that require an open connection, you can improve the performance of your application by explicitly calling the Open method of the Connection, performing the operations against the data source, then calling the Close method of the Connection. You should strive to keep connections to the data source open for a minimal amount of time to free up the resource to be used by other client applications.
Ref:
http://msdn.microsoft.com/en-us/library/bh8kx08z(v=vs.71).aspx[
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