InDesign Desktop on AWS

Yes it should be possible. I found the following

Adobe support and licensing terms w.r.t. installing on virtualized environments 

https://helpx.adobe.com/enterprise/kb/technical-support-boundaries-virtualized-server-based.html

AWS docmentation for such use cases using Amazon App Stream

https://d1.awsstatic.com/whitepapers/running-adobe-creative-cloud-on-amazon-appstream.pdf?eucd_src3

I suppose this should give you enough to investigate more and try your installation. Do let us know of the progess as well, so that someone else having this question is helped as well

-Manan