I doubt you will have any hard data on it, so I will add some thoughts on it.
First, you don't use DI (or other SOLID principles) because it helps you do TDD. Its the other way around, you do TDD because it helps you with the design - which usually means you get code that follow those principles.
Discussing why to use interfaces is a different matter, see: http://stackoverflow.com/questions/667139/what-is-the-purpose-of-interfaces.
I will assume you agree that having your classes do many different things results in messy code. Thus, I am assuming you are already going for SRP.
Because you have different classes that do specific things, you need a way to relate them. If you relate them inside the classes (i.e. the constructors), you get plenty of code that uses specific versions of the classes. This means that making changes to the system will be hard.
You are going to need to change the system, that's a fact of software development. You can call YAGNI about not adding specific extra features, but not on that you won't be needing to change the system. In my case that's something really important as I do weekly sprints.
I use a DI framework where configuration is done through code. With a really small code configuration, you hook up lots of different relations. So, when you take away the discussion on interface vs. concrete classes, you are actually saving typing not the other way around. Also for the cases a concrete class is on the constructor, it hooks it up automatically (I don't have to configure) building the rest of the relations. It also allows me to control some objects life time, in particular I can configure an object to be a Singleton and it hands a single instance all the time.
Also note that just using these practices isn't more overhead. Using them for the first times, is what causes the overhead (because of the learning process + in some cases mind set change).
Bottom line: you ain't gonna need to put all those constructor calls all over the place to go faster.