You will be required to complete a pre-commissioning physical. You must be mentally and phyiscally healthy in order to serve in the military so if you are receiving any treatment for illness they will be interested in knowing. This doesn't mean you will not be physically qualified because you have a cold when you take your physical. But if you have a chronic illness that is a problem (most common is probably high blood pressure). Call them and ask someone there, it won't be the first time someone has asked this question.