I realize this is a necro response to a 4-year-old post, but it's what came up when I searched the same question, so I thought I'd add my experience.
I was able to get PT4 working on an AWS PostgreSQL RDS with no problem. I'm using the free tier eligible configuration (db.t2.micro, 20 GiB storage, 1 GB RAM) and I don't notice any lag. HUD pops up a few seconds after the hand ends, just like when I used a locally installed DB.
The only caveats are:
- Don't choose a PostgreSQL version above 9.6. I'm using 9.6.20.
- Make sure you properly configure inbound and outbound rules so the server can be reached by your IP address. (VPC settings)