Hi.
In terms of MSIL, there is already a performance hit just doing an intermediate language.
To answer your question, yes they do cause a delay. Multiple inheritance, and a deep inheritance tree hits performance due to the virtual tables (in the words of C++). Similarly with interfaces and everything OOP.
MSIL(think OOP in assembly) is somewhat lowlevel already with regards to assembly, and it is meant to be close to assembly syntax as possible to reduce the performance hit to native code. Ultimately it still applies the same techniques as assembly on how it implements OOP.
Double Whammy.
The situation isn't that bad because the performance hit isn't significant enough on today's computers to cause a big hit. Usually it's the construction of huge objects, complexity (i.e. big-O), and various memory issues are the main causes for performance hit. With proper architecture design, you should not even come across any significant performance drop.
With that said, maintainability still outweights performance in terms of business applications, but if you're talking about hardware drivers, or things that require intricate performance gains, then structured C is still the way to go.
Currently CPUs are getting faster and faster, and applications are getting bigger and bigger, and it is the duty of a language to abstract the "how" out of the language and you decide the "what". Let the language worry about performance and implementation. That's another story to be told another time.
I hope that helps. Do ask more questions. :)