Mostly the case, but remember that you might end up working during odd hours. I live in Europe and remote for a US company. I pretty much get up/work/eat/sleep PST time.

The way I see it REMOTE often stands with "compatible timezone remote".

I wish there was something like "INTERNATIONAL REMOTE" which would allow us people in totally different timezones understand if the company is globally distributed/remote or not, because you might have issues if their working style is not compatible.

Remote should mean anywhere in the world but expect that some companies will prefer people who can visit a local or head office regularly, or people who work in a similar timezone or country to make things easier to coordinate.