CDN enables a user to fetch content from a CDN-POP that is geographically closest to the user thus allowing lower read latencies.
Without a CDN, every request would reach the origin server (in your case Azure Storage). The low latency offered by CDN is achieved when there are cache hits. On a cache miss, a CDN-POP will fetch the content from the origin server reducing the latency benefit offered by CDN. Cache hits are usually dependent on whether the content is static (results in cache hits) or dynamic (results in cache miss) and its popularity (hot objects result in cache hit).
Your choice of using a CDN or not depends on a) whether your files are static or dynamic, if dynamic then the benefit of using a CDN is lower b) whether low latency is important to your application and c) Request rate : With low number of requests your files are likely to be cached-out so a CDN may not be that useful and d) Whether you have high scalability requirements. Note, Azure storage has the following scalability limits. If your application exceeds the scalability limits of azure storage then it is recommended to use a CDN