I firmly believe that learning any functional programming language will boost your skill as a programmer. Since you're already comfortable with C#, learning F# will be made easier because you already recognize the .Net part of the language. You can even integrate components built with F# into other .Net projects.
Before I started learning F#, I was only able to think step-by-step. As I became more proficient at functional thinking, you could say that I became enlightened (hmm. this may sound a bit over the top, but it's true).
Working with immutable lists, for example, really boosted my understanding of recursive programming; something I never really thought about before. Working with list comprehensions and map/filter operations greatly helped me understand the principles behind LINQ.
I unfortunately can't use F# in team projects, but the ease with which I can now use/understand LINQ and other functional programming concepts aids my C# development.
I also used F# to build prototypes: F# interactive was a great help here. I've built and tested an algorithm piece by piece in F# and ported it to javascript later. Thinking about having to build it in javascript from scratch makes me shudder.
Short version: learn it. It will warp your mind (in a good way).