Yes you can, lots of functional languages work without mutation. I'd go as far as to say mutating should be the exception, not the default, in more traditional languages.
Go misses almost all tools a functional programming language offers (no iterator or combinators of any kind) and even if you really wanted and decided the verbosity wasn't a problem for you, I'm pretty sure the compiler doesn't optimize it well (it does a lot less optimisations than LLVM for instance).
But those things don't make a language functional. It's like saying there are no lambda statements as there is no lambda syntax, but syntax != feature.
I mean I see your point, and if I really wanted to be fully functional I'd use a language _with_ those things like Haskell. But not being mutable is easy in Go too.