can this be used to spread over an existing St Augustine lawn?

I have fescue grass and it works great with our type of grass. If the sod company used the top soil and compost mixture before and the grass lived, then that proves it will work well with St. Augustine grass. You could try mixing both over the top of the St. Augustine grass that is dormant or dead. If any of the grass has roots, it's just dormant and will come back with watering as long as you're not in a heat wave. If the grass is truly dead, then it won't come back and you'll need to reseed or resod it. I also suggest using a seed blanket after re-seeding if you decide to seed it and not use sod. This keeps the soil in place, keeps the bird and animals from eating the seeds and it's biodegradable. It isn't all that expensive when you think about having to repurchase and reseed an area after it was blown or washed away. But weigh the cost of it against purchasing new sod. Definitely go with the seed blankets over top of the reseeded areas using a mixture of compost manure and topsoil then spread the seed over it, but the blanket over it and then water daily if it doesn't rain. Seeds do need a certain outdoor temperature in order to grow.