Theoretically, yes, which is one of the reasons Obamacare requires people to be insured. The reasoning is, if you don't have health insurance, you'll be forced to go to a hospital emergency room (ER) if you're seriously ill or injured. Hospital ERs aren't cheap; they cost much more than a typical office visit to your physician. Plus hospitals are required to treat everyone, even if they can't pay. So if you are treated and the hospital picks up the tab, those costs may be spread around on everyone else's hospital bills.
Another reason for insuring as many people as possible is that this helps spread the risk. To keep costs in line, it helps to insure a lot of healthy people along with high-risk folks. Everyone pays in, but since the healthy folks won't use their insurance that often, the insurer will be able to pay the numerous and expensive claims of those with a lot of medical issues. But if health insurance is voluntary and a lot of healthy people opt out, that might leave insurers with mostly sickly, high-risk customers. If most customers are constantly submitting claims, that will drive up the cost to the insurer, who will likely pass those costs back onto the consumer [source: eHealth].
Some refute these assertions, noting that under mandatory insurance, health care costs will definitely rise for some people — those who currently don't have insurance or had a low-cost, high-deductible plan and now must purchase more to meet the mandate's minimum coverage requirement [source: Cannon]. Also there's evidence that there aren't enough primary care physicians to treat all the newly insured people. ER visits have actually increased since Obamacare took effect [source: Ungar and O'Donnell].