Yes, it is possible to host Sawtooth surveys on AWS. However, our tests have been limited to EC2 instances that are configured with the necessary software to run surveys on a single server.
You can host Sawtooth surveys on any hosting platform that will allow you to configure a web server that executes Perl through the CGI protocol and to allow that web server to connect to a SQL database server (MySQL or SQL Server are supported). See sawtoothsoftware.com/server-setup for technical requirements.
How you approach that using a given cloud hosting provider's service offerings is up to you. Some of the popular services that attract people to a given provider might not work with our survey software, but with the right technical knowledge, our surveys can be run in a variety of environments.