An aluminum downspout and extension will flex and the grout and tesserae will pop off. I once contemplated using my old extensions, filled with concrete, to make a fountain; but that's still on my to-do list.

If you just used half marbles (glass blobs) with silicone adhesive and didn't grout, it might last for a year or two.

I know that the extensions are flexible, but if I bent them into a snake shape before embellishing, and then left them alone, wouldn't they not flex anymore? I don't plan to disturb them once they are placed in the garden, although I do need to connect the extender to the original downspout to make it functional, so maybe the rush of water would rattle it a bit.

Expanding and contracting from the heating and cooling normal to a day will "move" them. Not to mention various critters like rabbits, birds, and squirrels . . .

If I did it, I'd just skip the grout which is from where most of the problems would arise.

NCCMAMA, could you use the concrete splash guards for gutters to make your snake? So it looks like the snake is coming out of the gutter.