Yes you can do it, since with an ObjectDataSource YOU ae the one writing the code that does the insert. Inside your "Update" and "Delete" methods you can simply perform two database actions, one for each database that you are working with. You can abstract this out to an operation that could be passed a connection to ensure that you don't have duplicate code sitting everywhere.
NOTE You CANNOT do this thought via a single connection, you must do two fully separate database actions.
Example
Per the comment there was a request for more detail.
Basically inside each of your methods, simply do two db calls, a crude AND NOT properly formed example to show the concept is below, for a "delete" method.
public void DeleteMyObject(int objectId)
{
SqlConnection connectionOne = new SqlConnection("MyFirstDbConnection");
SqlConnection connedtionTwo = new SqlConnection("MySecondDbCOnnection");
SqlCommand myCommand = new SqlCommand(connectionOne);
myCommand.CommandText = "DELETE FROM myTable where myid = " + objectId.ToString();
connectionOne.Open();
myCommand.ExecuteNonQuery();
connectionOne.Close();
myCommand.Connection = connectionTwo;
connectionTwo.Open();
myCommand.ExecuteNonQuery();
connectionTwo.Close();
}
Obviously the usage of a stored procedure, as well as proper using statements or try/catch is needed, but this gets the idea across.