Feeding strictly on Tea

I'm only flowering the plants and I don't want to go through the process of making a soil mix. I really don't want to use Miracle Grow. My plan was to just buy some Topsoil, Perlite, Peat Moss, and Water Storing Crystals. There aren't any nutrients in that mix. Can I supply these nutrients through compost teas alone?

For a while

You need a good base soil with plenty earthworm castings at the very least. Blood meal and bone meal are cheap.