High Max, there is some truth in what you are saying, but it doesn't apply to nearly all symptoms and diseases.
Taking a fever lowering substance (such as ibuprofein (Burana, Ibusal) or pseudoephedrine (Duact, the favourite medicine of Finnish Defense Force) when you're running just a low fever, it can indeed increase the time your body requires to defeat the infection. Especially if you take these drugs in order to feel capable of working, and refuse to stay home and rest. However, when running a high fever (depending on age and general health condition), treating the high fever might be more important than worrying about prolonging the infection, as fever can put an undue stress on organs like heart, kidneys and other assorted stuff. The fever can kill a person even if it's a natural response; however I won't deny that many people are a bit too pill-happy for treating the inconvenient small fever they get from the common cold. Letting it run it's course and just resting when you feel like crap anyway tends to make the disease go away a bit faster, since higher temperature kills the disease dead.
Same goes with medication that helps clear the airways. In a typical common cold, the upper airways mucous membranes are infected, which causes them to swell and be filled with liquid, which both increases the secretion of mucus and constricts the airways; this is why the nose is easily blocked. Taking something that reduces the swelling of the mucous membranes relieves the mechanical symptom, but I don't think it significantly affects the rate at which the dead infectants are removed from the body. It's main effect is making it easier to remove them from the nasal cavity and other parts of upper airways (including sinuses). Besides, the mucus mainly contains
dead infectants anyway; the actual work to kill the infection is made on cellular level and the increased mucus secretion is just a result of that.
Cough medicines typically make the sticky mucus stuck in your lungs come loose easier, letting you get rid of it easier and thus reducing the coughing; remember that excessive coughing can cause mechanical damage to the lower airways (sore throat, coughing blood in extreme cases) without actually getting anything done if the mucus is just stuck there, irritating your airways and prompting the cough response again and again. It also spreads the infectants to the surrounding area very effectively by aerosole spread, and treating it is definitely worth it. It isn't an integral part of the healing mechanism that eventually destroys the infection internally.
...Aside from that, you can't really "train" your body to be resistant to stuff like common cold or flu virus infections. They typically mutate between the seasons so that your immune system is just as unprepared for them as it is for other stuff. Not treating symptoms does nothing to your flu/cold resistance. However, you
can keep your natural defenses high by eating healthily and staying in good shape, which all contribute to the effectiveness of your immuneresponse level.
Of course, there's always the possibility of the flu virus causing a
cytokine storm and then your strong immunity system can cause more damage than the infection itself. In fact, that's what killed significant portion of the victims of the 1918 flu infection (along with bad hygiene and overall conditions that contributed to both the spread of infection and general condition of patients).
