If the terms of the GNU Public License are complied with, it should be reasonably clear if a device is using any GPL code, including Linux, moreover the source code should be available too.
If the device uses an OS that is not open source, then even if the information were available to you, it is unlikely to be particularly useful except perhaps in respect to applying manufacturer's firmware updates.
Linux is by no means that common in embedded systems in general. It is commonly used in certain types of device, such as routers, STB's and NAS's. Often these devices have a web-server interface through which version information is usually available, but there is no common method of accessing this information, you'd have to access the particular URL for the device and parse the HTML.