No, it is the shoots which are eaten. Thet are just about to come in season here, though you will see stuff flown in from Peru or mars or somewhere far far away in the supermarkets. The asparagus plants' roots are spidery an far reaching which is why they don't transplant well. New plantings take a couple of seasons to establish before they are cropped. They are however perennial so once established and happy should crop for many years to come.