For 3 weeks with the pump off, even if you start out at high shock of, say, 20 ppm and add polyquat 60, you will come back to a green pool. Even with a loaded floater in the water. If the water isn't being circulated, it's stagnant, and stagnant water turns green.
But hey, so what? You KNOW how to deal with a green pool!
I go away for 6 weeks every year during August/September. When it's still really hot here. I dose the pool to 20 ppm, put on the solar cover to keep leaves out, turn off the pump, and drive away. I don't want to impose on neighbors, I don't have friends who live close by (though they live close enough to come swim on the weekends, of course). I turn off the pump because we have a lot of power outages here in the summer and I don't want a surge to wreck the pump. Or for something to get sucked in or whatever can go wrong with pumps (the sky falling?) . . . so I turn it off.
Yes, the pool is a deep jade green when we get back. First order of business while husband unloads the van is to turn on the pump and pour in 3 large jugs of Clorox. The next morning it'll be a light green. More bleach, more time, brushing, more bleach, and by the end of a week it's crystal clear again.
Don't sweat it. It's only a pool. Have fun on vacation and have Clorox handy for when you get back.