Please take this answer with a grain of salt, because I'm no expert in aquariums. But approaching this question from a purely logical angle, the answer is a resounding no.
An aquarium is a mostly-closed ecosystem with stagnant water. All organisms share the same water and have to survive it. Unfortunately fish have to poop in the same water they live in and the chemicals in the poop will eventually poison and kill them. Especially gold fish are known to be a "dirty" species, producing a lot of waste products.
When you set up a new aquarium you have to cycle it for some time (usually several weeks) in order to allow a special type of bacteria to grow in proper quantities. These bacteria will feed on the fish poop and transform it into chemicals that are harmless for the fish.
You can use potting soil in small quantities for your aquatic plants, but if you use only fertilized soil for an aquarium, one of two scenarios (or both at once) are likely to happen:
- Since your soil is fertilized with goat's poop, it could kill your fish quicker than the beneficial bacteria can clean the water.
- The soil could cause an algae bloom in your aquarium, clouding up the glass and potentially killing your fish by other means.
Consequences [of an algae bloom] range from the benign feeding of higher trophic levels to more harmful effects like [...] causing a depletion of oxygen levels in the water, and, depending on the organism, secreting toxins into the water.
I think the best approach for a beginner is to think of the aquarium as a space habitat or a closed ecological system for your fish. Eventually you want it to be independent of outside influences (like water changes), so you have to plan accordingly an be aware of how each component in it affects the whole system.
Something as seemingly unimportant as the choice between mineral sand or coral sand as a substrate can have a devastating effect on the ecosystem in an aquarium.