In theory yes. In practice no. The duty free allowance for UAE is a massive 4 litres of spirits. Don't think any other country allows that much allowance. ( The UK allows only 1 litre BTW)
As long as you don't get drunk and create a ruckus you will be fine .
PS: I have never heard of any tourist being prosecuted for carrying alcohol in Dubai. However if you are intoxicated and get into trouble then you 'could' be charged for this .
Perhaps m3red or other Dubai residents might be able to confirm this?