In which countries would "tags" be understood to mean "License plates and stickers that show the registration is currently valid"?

It has that meaning in the US, although it's a bit jargon-y. Most people will say "plates", but most will understand "tags" at least in context. When you buy a car at the dealer you pay a "tag and title" fee through the dealer to have the car registered and receive a license plate, and the shops that exist in some states to handle registration paperwork outside of the DMV offices are usually called "tag and title service". You might also hear a policeman report something about "a white Chevy with Michigan tags."

Despite how it may seem, "tags" does refer to the license plate, not specifically to the sticker or decal that's attached to the plate to show that the registration is current. Wiktionary is in agreement with me on this one (ety 1, n. 8.)

I can't speak definitively for other countries, but certainly in Canada and the US, referring to a car's "plates and tags" indicates their license plate, which generally lasts for multiple years (my state replaces my license plates every 7 years) and their registration renewal tag, which is a smallish sticker (about 3cm x 5cm) affixed to one corner of the plate; the tag displays the year number of its issue, so if a police officer examines your license plate and discovers that its tag is not showing the current year, he can cite you for driving with an expired registration.

The Wikipedia article on vehicle registration plates only calls out the US as an example of countries requiring the use of a sticker (they call it a decal on the page) to indicate the year of registration. I flipped through some of their "License Plates by Country" pages and did not find anyplace besides Canada and the US where registration stickers were visible in the sample images.

The only place I've ever heard someone call a license plate a 'tag' is in Alabama when I visited a friend of the family there. I've never heard anyone use that in the Midwest or West. I think it's southern slang, but it's so very common there that no other word is used.