Should I list this experience?

So I did an Equity Research intern in a very small startup firm. The company only has 4~5 people including HR. I applied for this job on my school career site and got the job. The process was relatively informal: phone interview and in-person interview. The manager just called me for the offer but didn't send me a formal offer letter. I worked for them for 3 months and participated in a 3million deal. I think putting that on my resume would be helpful. Then I got a very series health issue, my back hurt so bad that I couldn't stand and even sat properly and had to go to a doctor for treatment. Unfortunately, I couldn't continue the internship due to that reason. But I'm wondering can I list that experience on a resume? will that affect my background check since the whole process was so informal? Also, there is no specific length for this intern, I can leave any time. It's just that I ended earlier. The only thing I worried about is the background check....