In order to do a study about quantities of boilerplate code, you'd first need a definition of boilerplate. If you want the study to be completed during your lifetime, the definition will need to be something that can be checked by a computer. You'd also need access to a lot of code. However, not all code is publicly available, so there's a possibility of selection bias. Finally, what would be the benefit of the study to justify the cost?
That said, I would think the amount of boilerplate code would be more tightly correlated to the programming language used than the type of project. A website created using Lisp, for example, would have a lot less code than a website created using COBOL.