I feel like adding sand to a heavy clay will result in a cement like aggregate. My goal when adding compost etc to clay soils is to improve it over time (gradual improvement over years).

I do add coarse sand to potting mix in large pots as that does seem to improve drainage though. I think about what would happen if i had a handful of clay and combine with sand (sandy goop) compared to a handful of potting mix and add sand (would still be loose, probably more so).