To answer the original post, yes it can. It will be living in the water on the plants. Try washing your plants in salty water, or in a diluted iodine solution.
For the poster above, you have a real mess in there, which has small chance of survival, especially where dropsy is concerned. IMO, euthanas the fish that get dropsy, it's very contagious, and can easily transmit between tanks. Add 1 teaspoon of salt per 5 gallons of tank water, but spread the treatment over 3 days so as not to shock your fish (for example, a 9 gallon tank, add 3 teaspoons on day, then another 3 on day 2 and so on) Remove some water from the tank and dissolve the salt in it before putting it in the tank. When you do water changes, add the salt to the new water (ie, if you remove 2 gallons, add 2 teaspoons back)
This method is better then adding half a dozen meds to your tank, and will help remove infections through osmotic pressure.