I don't think giving your immune system merely more energy will work as you intend. All it will do is performing what it already does more quickly. So yes, a flu might be fought off before it has time to actually break out. Your cold gets stopped before it gets started.
However, there are quite a few diseases thanks to the immune system not recognizing something that needs to be fought off. Cancer is one of those examples -- the cancerous growth is not recognized by the immune system as cells to kill off, and so it can spread. Immunotherapy already exists today and can be used to make the immune system kill off cancer; however in most cases it requires outside help like certain proteins that paint a target on the cancer cells.
Another example of the immune system not recognizing something would be HIV. The virus infiltrates the immune system itself, and masks itself as immune cells. Does that mean that the HIV cells also get the unlimited energy!?!
Additionally, unlimited energy might make your immune system overactive. I am not talking about the time when the immune cells go into a kill-invader-frenzy, but when they are so bored/misconfigured that they target benign substances. This can result in allergies (hypersensitivity) and autoimmune diseases (attack useful body cells like lung tissue or nerves). Not to mention that organ transplants will be rejected nearly immediately.
So, unless you don't only give your immune system more energy but also a better targeting system, you will definitely not make humanity disease-free.
Might create an interesting setting though, where you have to decide: do I want to boost my immune system until that darn cold's gone, when there's the risk of rejecting my transplanted kidney / developing an allergy / developing an autoimmune disease? Or: This illness is so severe that we MUST work with an immune system boost -- but we must be really careful that we don't worsen the existing allergy / autoimmune disease to the point where the allergy becomes more deadly than the illness.
Symptoms of an immune system in full 'fight-off-invader' mode:
- fever (raise body temperature to make life more inhospital for invading organisms)
- swollen lymph nodes (lymphatic system transports a lot of immune cells)
- high white bloodcell count (might be raised to a ridiculous degree in your case since you've got unlimited energy to produce more -- which might carry its own issues)
Allergies are NOT a symptom of an active immune system!