Using a H1 helps Google establish what the page is about, it is not a sole factor and one of many... As long as Google has many other signals then its not a problem. In terms of the impact its impossible to answer since no one really knows how much but people believe the headers to be less important as the meta description and title since these pop up in Google Search.
It's worth checking out this table from one of my favorite SEO New sites (Click the image to view large):
So in other words its possible to rank a page without headers.. However headers tell Google better what the page is about, so assuming that everything else is right then Google should be able to rank it, it may take a little more SEO work such as off page SEO to get it to rank better but as I said its not a sole factor and everything is taken into account, you will not find a percentage of how much it will prevent you ranking as such as this is Google's algorithm which is constantly changing never mind one of there prized secrets.
