No, it's not available everywhere. It won't work in a country it's government has it blocked, as in China, for example. Said so, I have no idea if the government of the UAE has Grindr in its blocked list.
Grindr does not work in the UAE, Qatar, Saudi Arabia, China, and a few other countries. It does work in Russia, Belarus and other former Soviet countries.
In addittion to a multiband GSM/WCDMA phone (unlocked of course) , the true global gay jet setter absolutely needs a VPN (Virtual Private Network), which will issue you an IP address based in the US, or Western Europe, anywhere in the world.
Your idevice (or blackberry) can be configured to acess the internet via a VPN. You can use this to watch Hulu, Netflix etc, and unrestricted contect of "interest", sans censorship.
A search in the "travel technology forum" should get you stated.
Location: شمال أمريكا والعالم العربي - N America + Arab World
Programs: *A, SkyTeam
Friends use Grindr in Saudi all the time. It's not as popular as gaydar or some of the other websites - though, so my understanding is it's the same few ppl who are on it all the time. Of course, the numbers may have multiplied since I was last there in December.