I strongly believe that learning a new style of programming will make you a better programmer. F# has been on my radar for a while and I am contemplating a dive, shallow or deep I have yet to determine.
Yes, F# can possibly help a lot for certain classes of applications, but I do not know how much, if any at all, for line-of-business apps. My understanding is that F# is well suited for math and science applications and its functional nature can help write more reliable concurrent programs. Given the increasing number of multi-core processors, this might be prove valuable.