At this time yes you can. However that is soon to change. Beginning in January of 2014 the affordable care act mandates that no one can be denied coverage based on pre-existing conditions. You will be able to take out a policy in or out of the exchange. You also cannot be charged more premium because of your health.
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As a result of Obamacare, most states do not have child only health insurance plans.
In most cases you cannot be denied employer group health insurance plan coverage.
All this will change in 2014 when carriers cannot deny you but expect premiums to be 2x current levels.