Hello Kimon,
Yes, ASE product editions can be installed, configured, ran within the MS Azure cloud.
KBA 2134316 - Can SAP ASE run in a cloud environment.
KBA 2262776 - Can I install ASE Edge Edition on a machine with more than 4 cores?
https://service.sap.com/sap/support/notes/2134316
https://service.sap.com/sap/support/notes/2262776
Regards,
Michael