No, the overhead will be in how to best map the F# to the C# code all the time while reading C# docs versus just not having this mental juggling in C#.
There's barely any overhead to consuming c# libraries from f#. You type "open SomeLib" instead of "using SomeLib;" and "let x = SomeClass (foo, bar)" instead of "var x = new SomeClass(foo, bar)". You check return values with "match Option.ofObj value" instead of "if (value != null)".
