There are at least 3 kinds of diseases we run into in the aquarium hobby.
There are parasites that need to be introduced on plants, decor, new fish or similar means. Ich is one of the parasites that must be introduced in order to be present.
There are bacterial and viral infections that again must be brought in by outside introductions. None of these can suddenly show up in a healthy tank unless something new is added to the tank. One of the possible sources of contaminants is live or frozen foods. although most are fairly safe to use, it is a possible source.
The final type of disease can hit any tank even if nothing is ever added, it is chemical damage and or deficiency diseases. This group is the result of either poor diet, water conditions not being properly maintained or contaminants entering from the air such as happens when you don't think about the fish and go about painting the room the fish are kept in and the fumes in the air get into the water.
If you are not introducing any new fish, the third type would be the only ones you would normally need to worry about much. It is not only possible but quite normal to have a disease free aquarium. To maintain such an aquarium, you need to have a quarantine tank so that, if you get a plant or fish that is carrying diseases or parasites, you can intercept the problem before it gets into your main tank.