It is quite normal to change the appearance of html elements with css. I believe that search engines are mostly style agnostic, except perhaps where it is used for hiding or cloaking content. But the point being it is the html that defines the document structure, so content wrapped in
<h1> is considered the primary heading of a page or article no matter what size the css tells it to be.
My only concern is how things will look to real human visitors from a UX point of view. You are free to style your site any way you like, but users would expect the main heading (or any heading) to be distinguished in some way from ordinary body text. Making it the same size as body text won't help that, though there are many other ways like bold, italic, different font or colour to differentiate it. Using the same size does not offer much scope for styling different levels of header, if indeed you have multiple levels of header. It does not have to be the full default size of h1, but it may be a good idea to make it at least a little bigger than normal text.