gRPC "works" in AWS. That is, you can run gRPC services on EC2 nodes and have them connect to other nodes, and everything is fine. If you are using AWS for easy access to hardware then all is fine.
What doesn't work is ELB (aka CLB), and ALBs. Neither of these support HTTP/2 (h2c) in a way that gRPC needs.
ELBs work in TCP mode, but you give up useful health checking and the join-shortest-queue behaviour that makes normal HTTP mode ELBs good. It also means you may experience problems with how well balanced your cluster is since only individual client connections are balanced rather than individual requests to the backend. If a single client is generating a lot of requests, they will all go to the same backend rather than being balanced across your available instances.
This also means that ECS doesn't really work properly since it only supports the use of ELB and ALB load balancers.
If your requirements are not too demanding TCP mode ELBs do work, and you can definitely ship stuff that way. It's just not ideal and has some fairly major problems as your request rates and general system complexity increase.