Is it possible in Entity Framework MVC application to run .sql scripts on a different database

This might help you The number of tables only affects EF initialization where "views" must be compiled when the context is used first time in the application - 400 is a lot and it will take a lot of time. This can be speed up by generating source code for views and adding these source codes to the project - views will not be compiled at runtime because compiled code will be part of your application but you must manually do this each time you change the model. For EFv4.1 this feature is offered in EF Power Tools CTP1. For EDMX the feature is offered in EdmGen command line tool.
Another impact on such number of tables in on development. Using 400 tables in single EDMX seems impossible so you will need multiple contexts with different sets of mapped entities. This can be complex task for application architecture because working with multiple contexts makes everything harder.

seems to work fine I think this is related to the connection to the database. Entity Framework checks for an existing database that you defined in the context class that inherits from DbContext. If it does not exist Entity Framework will create it locally for you in development. But when your ready to deploy your application you need to define the connection string to the database. Since your are using Entity Framework Code First I would also recommend using the Entity Framework Power tools that you can download from NuGet. You can read more on the DbContext, and setting up the models here. Entity Framework Code First Context
I would inspect this aspect of the article:

public class BloggingContext : DbContext 
{ 
    public BloggingContext() 
        : base("BloggingCompactDatabase") 
    { 
    } 
}

hop of those help? After trying all these, I recreated the solution which I used to keep model classes and now I am able to add model. Problem solved.

this will help I have a unique (or so I think) problem - we have an ASP.NET web app using MVC principles. The project will be at most single threaded (our business requires single point of control). We are using Entity Framework to connect to the database ,
How would you recommend connecting to the database?

around this issue I figured it out. The MigrationsNamespace isn't the same as the namespace of ApplicationDbContext. I had to explicitly put the namespace where all the migration files reside. Also, when instantiating the configuration, I had to include the proper context key. It works now and looks something like this:

var database = new ApplicationDbContext().Database;
        var configuration = new DbMigrationsConfiguration
        {
            TargetDatabase =
                                        new DbConnectionInfo(
                                            database.Connection.ConnectionString,
                                            "System.Data.SqlClient"),
            ContextType = typeof(ApplicationDbContext),
            MigrationsAssembly = Assembly.GetAssembly(typeof(ApplicationDbContext)),
            MigrationsNamespace = "Prom.Database.Migrations",
            ContextKey = "Prom.Database.Migrations.Configuration"
        };