Its possible dear, i also faced that problem one time. I just want to know in what circumstances google do that.. and the impacts..
if you are blocking the Home Page via robots file or noindex then it may be possible but i have never come across such website. further, if the Home Page is blank then may be Google keep that page out of its index. as far as impact is concerned, first impression is the last impression. if your Home page is full of flaws or is empty then no level of SEO/SEM can create good image of your website in user's mind