Could I use butternut squash? Would timing change if so?

I have found that butternut can be quite a bit harder than kabocha, taking longer to cook. The time required for the barley to cook may be long enough to cook the butternut, but the butternut squash may not be as broken down as the kabocha would be. You might therefore want to extend the cooking time 5 - 10 minutes, as necessary, to reach the level of softness you prefer in the squash. ;o)

Of course, yes.
In most recipes, winter squash varieties are interchangeable.
But if you have a choice, or no aversion to it, the original kabocha usually has more flavor.