Does AWS support multicast and IGMP snooping?

Historically, AWS VPCs have not supported multicast.

The AWS engineers have recently developed a proof-of-concept multicast overlay, that has support for IGMP snooping.

See Overlay Multicast in Amazon Virtual Private Cloud

This is only proof-of-concept and is not yet fully supported.

Update as of December 2019, Yes, AWS now supports Multicasting via AWS Transit Gateway

https://aws.amazon.com/about-aws/whats-new/2019/12/run-ip-multicast-workloads-aws-transit-gateway/

https://docs.aws.amazon.com/vpc/latest/tgw/tgw-multicast-overview.html