No, C# has plenty of features making functional programming possible, so it is definitely on the spectrum of FP languages.
Let’s go at it from the other direction - is Haskell functional? Because it has unsafe pointer access and unsafe IO, so it can pretty much express every C# program as well, right?
Would you agree that C# is not functional?
If you agree that C# is not functional, than F# is also not functional. Nearly every construct that can be expressed in F# can be expressed in C#.