Not out of the box - serverclasses can only use a small number of variables to control membership - such as name, IP address, OS.
There are two general ways this could be achieved, but both require a bit of programming to get working
Create a script to generate the serverclasses.conf content which has the required mapping. This would use data from Azure to identify which hosts have which tags and link them to the relevant serverclass. Then run the splunk reload deploy-server command to get the config active in Splunk. You script will need to pull the list of tags and hosts from Azure or maybe even you can use an existing Azure add-in to retrieve this data from Splunk.
Use the "clientname" option in deploymentclient.conf to append a tag name to the computer name and then you can use the built-in wildcard options in the serverclasses.conf (or web interface). You will need a script running on each host to get the tags associated with that host and write that data to a local deploymentclient.conf file. This option is only workable for one or two tags per host.