If I buyan Apple Watch GPS cellular in Italy, will it work in DUbai?

Did you check the linked article about the carriers that support the Apple Watch?

These are the carriers available in the UAE, and you will have to make sure, that your plan includes the use and support of the European model of the Apple Watch. Looking at the LTE hardware, the Apple Watch SE, Model A2725 (40mm) and Model A2724 (44mm) at least support the same LTE Bands for both regions.

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copied from: Apple Watch - Carriers - Apple

You should always buy the Apple Watch in the country in which you want to mainly use it.

The built in hardware has to support the local carriers and their services:

Apple Watch - Carriers - Apple

Plus, the warranty is restricted to the country of purchase. If you have a warranty claim, you will have to send the watch back to the country of purchase, Apple does not ship internationally.

In theory it should work, HOWEVER, it is totally up to the carrier(s) in the UAE if they want to provide service for the watch.

For example, if they realize that watch has features that are restricted on UAE sold Apple Watches, they could choose to refuse service, least they get in trouble with the government. Just guessing at why they might refuse service.

No.