Is it alright to use CSS3 with HTML4. It seems like CSS3 would be a HTML5 complaint deal. But I'm not sure if that's the case.
If it's not okay, what are the downfalls to using CSS3 with HTML4, opposed to CSS3 with HTML5?
Yes, to the extent that “CSS3” exists at all. “CSS3” is a collective name for a set of specifications and drafts at very different levels of maturity and implementation. There is no single CSS3 specification (like there is the CSS 2.1 specification), and probably never will. Thus, “to use CSS3” means very different things, ranging from well-defined universally implemented features to sketchy constructs with experimental or no implementations. Whether they work or not does not depend the least on whether you call your markup “HTML 4”, “HTML5”, or something else.