Beer's about the most unrefreshing drink going. It tastes dreadful and it doesn't nourish you in any way.
I've a box of ice poles in my freezer and the kids have hoovered up the orange, lemon, strawberry, raspberry ones. The only ones left untouched is cola - which is itself a horrible flavour when you extract all the fizzy bubbles. I reckon a flat beer flavoured ice pole would also be awful.
I type this as a beer drinker of 20 years who would drink 40 pints a week.