While I agree with everyone else that the safest option is to try to get some kind of insurance, I know from experience that this isn't as easy as it sounds. Not having insurance will not necessarily affect your AOS application, as long as you have other evidence that you can include.
When I moved here on my K-1 visa, my husband had not had health insurance for many years. His employer did not offer health insurance, he could not afford plans through the Marketplace, but his income was too high to qualify for Medicaid (he was in the "gap population": income too high for Medicaid, too low to be able to afford other plans). I moved here, and there were no affordable insurance options for me either, especially because we were living on just his income for months. I was very homebound because I was just waiting for my EAD and couldn't do much, but it was still a scary situation. As soon as I was getting close to receiving my EAD I started looking for jobs and specifically looked for employers providing health insurance. I was able to get a job offer even before I received my EAD, they were willing to wait until my EAD would be approved, and I started working the day after I had received my EAD. That job came with health insurance for both of us.
We had my AOS interview a few months after I had started working. We had initially filed my AOS without much evidence, but were able to bring the insurance policy and statements of our joint account to our interview and were approved.
Long story short, yes you should have health insurance if at all possible. And in some states it can be very challenging or simply impossible to find affordable health insurance. Having health insurance is not a requirement for AOS, but it may help as evidence.