Yes, and then you have an asparagus bed for 5-15 years. After the soil is depleted, you can't use that patch of soil anymore for asparagus for like 30 years. Source: my parents have always had at least one, usually two, beds of asparagus.
Only if you let it go. If you're cutting it for eating, it only gets as big as you let it. (And if you let it grow past normal eating size, it won't be very good to eat.)