Since you are using Compact edition, the way I'd go is to provide a complete new database, and transfer their data over, rather than trying to add anything to the existing file. That way, if there is any problem in the update, the customer doesn't lose anything.
In theory, adding a table programmatically to a DB shouldn't cause any problems anyway: it's just a case of issuing the CREATE TABLE command:
string sql = "CREATE TABLE NewTable (LastName NVARCHAR(40) NOT NULL, FirstName NVARCHAR(40) NOT NULL, EmailAddress NVARCHAR(256))";
And that won't affect existing data - but Databases can be delicate, as can the people who depend on them! I'd create a new DB completely, and make sure they are kept happy.