Be interesting to see. I'd assume the db is the bottleneck, would be nice to get stats on that. Should point the way to scaling more economically, i.e. well spec'd DB server and cheaper app server(s).
Could also use something like https://github.com/awslabs/pgbouncer-rr-patch to route read only queries to a replica without any application changes, although there's some nuances, e.g. it might need some finessing if the app writes and then reads in two sessions, expecting to see the results from the write in the read.