We haven't yet deployed a production network in Azure, but I think I have worked on couple of POCs.
To summarize the answer to your question "it depends on your network design". What factors may have an impact is as below.
1. Requires Azure learning curve. Most of the wireless engineers may have to depend on other teams to deploy/tshoot and manage the WLC.
2. WLC performance depends on Azure infra which as a customer you have less visibility, usually they are reliable, redundant and secure.
3. If the WAN is not properly configured to have AP to WLC communication, there might be issues. (Latency, MTU, VPN etc.)
4. No local mode support for the AP's. So, if you are migrating from a setup which has APs in Local mode it will require you to move to Flex connect.
5. OEAP support may require complex design and physical WLC's.
6. Authentication challenges, if you are using Central Auth *depending on the design you might have to move to Local Auth.
7. Azure support started from 17.7. So if you have Wave 1 APs in your network it will not support. Make sure that you read the release notes to understand what AP models are supported.
Advise - I have seen people move certain appliances to Public CLoud (Azure,AWS,GCP etc.) just for the sake of aligning to CTO/Management vision to have everything in cloud. It works for some, it doesn't for others. So do a proper and complete impact analysis to understand how the authentication will be done, what other complexities and changes required to accommodate this change in our existing network, latency to Azure from all the sites etc. before moving to any Public Cloud.
