Sorry to be a bit thick but this doesn't work as you described.
I installed the package, then I use my existing code first connection string.
<add name="MyDbContext" connectionString="Data Source=.\SQLEXPRESS; Initial Catalog=Databse; Integrated Security=True;Connect Timeout=300;Encrypt=false;Trusted_Connection=true;MultipleActiveResultSets=True;" providerName="System.Data.SqlClient" />
<elmah>
<errorLog type="Elmah.SqlErrorLog, Elmah" connectionStringName="MyDbContext" />
</elmah>
? Nothing is created in the database.
I delete the database and when I re run it EF creates my models but still the same error.