Yes, you can register .ae domain name(s) regardless of your presence in the UAE. .AE (and .emarat IDN are open zones just like a .com domain name).
We are an accredited .ae domain name registrar under the government of UAE's .ae registry, the ae domain administration (aeDA) - part of the TRA.
Here is what our terms of service TOS says:
.AE Domain name(s) can be registered by any individual/company. Local presence in the UAE is not required.
Please check the guide below for a more comprehensive report: