Yes, but "foolish" is an important component of US Cyclocross You will likely be able to get around the course without permanent injury and have a significant amount of fun. You will not likely be competitive in any category.

I doubt that toe clips would have much advantage over MTB platforms with good retaining pins and some shoes with soles they can bite into. Also keep in mind that when it comes to clipless, you don't need anything fancy. $100 is more than enough to get an adequate set of clipless shoes and pedals for CX.