fast grown crops may contain less nutrients. It really depends what fertilisers you are thinking of...artificial ones (chemicals) work faster and are generally cleaner to handle but may produce crops with a higher nitrate content which may not be healthy (you could research this) Natural fertilisers (manure, compost, green manures) work more slowly and may provide a more nutritious crop but manure fertilisers can carry parasites/diseases.
HTH
Fertilisers will help crops but will also help the weeds, which will lower your yields. Also, fertilisers could be washed by rain into streams and ponds, causing more water weed to grow; this will cut off the light to underwater organisms, which will die and rot. The water will then be full of rotting plants which can kill off animal water life. Try looking up eutrophication in your science text book.