Actually, there are two separate issues in this topic which are usually mixed: cloud (subscription) licenses and cloud location of the system.
The most interesting thing is that wherever the database is located - in a cloud or on-premise - you still can use subscription licensing method for NAV, introduced not so long ago. This means that you will pay (monthly) subscription fee and will be able to use all the newest versions of the software, regardless where they are located (no BREPs). This also means that you can very easy regulate the quantity of the licenses: if you have seasonal (or crisis) shrink of your users, you can consequently diminish the monthly payments, starting from next month, and increase them back when things go well and you get more stuff.
The other thing is where your database is located. It can be pure Microsoft Azure with all the benefits and costs of that, it can be some Azure Pack, ported to your country, or it can be some third party datacenter. Whatever licensing method you use, you can put your database either to one of those clouds or use it on-premise.
Then, project Madeira has been recently introduced, as a full SAAS model for small business, but it has yet very limited functionality and most likely it is not your solution so far.
Thus, answering your question - you might not necessarily pay Azure fees when using subscription licensing for NAV.