I'm also not sure what you mean by the line running to the beach... Were you just referring to the down line again going into the "beach" on the bottom? If you're actually talking about running it to the beach (dry land) that might not work so well....
We anchor 99.9% of our floats in sand with corkscrew anchors so that shouldn't be a problem! You just have to make sure that you have a good anchor and that you actually screw it in all the way. When done properly with a down line and then a tag line (running across the bottom - which can be an extension of the same line), i've seen a class of 10+ students all hanging on it (or rather getting dragged across the bottom...) with very heavy surge. The anchors easily held in just sand.
I don't know which type of corkscrew anchor you're using, but this is the type we use which works very well:
View attachment 130254
We usually use two, one at the bottom of the down line, and the other on the end of the tag line. The extra metal piece makes screwing them all the way in very easy (enough torque even in bad conditions). If you're just using a down line --> only one anchor. If you're worrying about the line getting away from you while you're screwing the anchor in, and you can't take a buddy down with you to hold it, take an extra 4 lb weight, clip it to that and set it in the sand. Just keep an eye on it, but it should be fine!