Depending on the health insurance company and the laws of the state where you live, there may be a waiting period after the coverage goes into effect before some illnesses and serious medical conditions will be covered. It is difficult to say exactly how you will be affected, and some policies are fully in force as soon as you have been accepted, so check with your insurance agent or the customer service department of your insurance company to find out how the company handles such claims.
Group health policies, such as those purchased through employer-sponsored health plans, are in force after you have been accepted. Typically, enrollment is only allowed during certain months, and waiting on the enrollment period qualifies as the waiting period under which you could have been denied coverage if you were diagnosed with an illness. However, since group health plans do not usually require medical exams or other medical qualifying, the diagnosis would not affect your coverage with a group health plan regardless.
Individual health plans are more stringent than group plans. You would have to undergo a medical examination before you could be accepted into the plan. If the medical exam discovered a preexisting condition, your insurer could decline insuring you, but if the exam did not reveal a condition your coverage would be valid. If you were then diagnosed with a serious condition after acceptance, the insurance would, by law, be required to coverage it as set forth in the policy.