I don't think a side channel attack against L4 would be particularly useful - the kernel's tiny, and doesn't really do much other than scheduling, IPC and capabilities. Anything you might want to learn lives in other processes.

That said, the big caveat of the whole thing, is that by pushing stuff traditionally considered to be sensitive to user space doesn't solve security or stability, it makes it other people's problem. There's no reason you couldn't do a side channel (or a different kind of) attack against a process that hosts the filesystem.