Linux by itself is not very useful because there are no applications: it is purely a kernel. In fact, when the kernel finishes booting, the first thing it does is launch an application called
init. If that application isn't there, you get a big error message, and you can't do anything with it*.
Distributions are so named because they distribute the Linux kernel along with a set of applications.
Likewise, the GNU utilities by themselves are not useful without a kernel. You could put them on a storage medium and turn on a computer, but there is nothing there to run those programs. Also, even if there were something that started
init and all the other programs rely on the kernel for services. For instance, the first thing that the program that is usually called
init does is open a file
/etc/inittab; to open that file, it calles a function
open(); that function is provided by the kernel.
Now, you can build a distribution that has no (or few) GNU applications. See Alpine Linux for an example. This is why I do not call Linux GNU/Linux; when I say Linux, I am not referring to the subset of Linux systems that have GNU utilities.
*Technically, there are some things you can do with just the kernel.