No.
When people say "Linux on the Desktop" they really refer to an ideology: a computer running the Linux kernel, the GNU system on top of the kernel, and server or application software running on top of the GNU system, with all software licensed under the GNU GPL.
Chrome OS certainly uses the Linux kernel. But the 'magic' of Chrome OS happens on the backend of Google's datacenters, and none of that software is GPL.
In fact, I'd say Chrome OS is the anti-Linux: a vendor (Google) creating a product that uses GPL software (the Linux kernel) when beneficial, and mixing in proprietary software (the back end services) when it isn't. While legal, this clearly violates the spirit of the GPL and the free software movement.
[BTW Qbertino, complements on your English.]