Can I increase the timeout by modifying the connection string in the web.config?
If you want to dynamically change it, I prefer using SqlConnectionStringBuilder .
It allows you to convert ConnectionString i.e. a string into class Object, All the connection string properties will become its Member.
In this case the real advantage would be that you don't have to worry about If the ConnectionTimeout string part is already exists in the connection string or not?
Also as it creates an Object and its always good to assign value in object rather than manipulating string.
Here is the code sample:
var sscsb = new SqlConnectionStringBuilder(_dbFactory.Database.ConnectionString);
sscsb.ConnectTimeout = 30;
var conn = new SqlConnection(sscsb.ConnectionString);